JSFHJSFH Tutorial C\303\241lculo Vetorial e Integra\303\247\303\243o M\303\272ltipla Parte 2 JSFH

JSFH Intimamente relacionada aos c\303\241lculos de fluxo de superf\303\255cie implementada pelo comando Flux, pacotes VectorCalculus do Maple tem um comando SurfaceInt para calcular integrais de superf\303\255cie. Fluxo de superf\303\255cie \303\251 apenas a integral de superf\303\255cie da componente normal de um campo vetorial sobre uma superf\303\255cie. O comando Flux determina a componente normal e o elemento de \303\241rea de superf\303\255cie. O comando SurfaceInt calcula a integral de superf\303\255cie de um escalar, e para isso ele determina o elemento de \303\241rea de superf\303\255cie apropriada. JSFH Como para o comando Flux, o comando SurfaceInt reconhece a caixa e esfera como superf\303\255cies fechadas, e prev\303\252 para a integra\303\247\303\243o sobre superf\303\255cies definidas sobre um disco, elipse, ret\303\242ngulo, tri\303\242ngulo ou regi\303\243o plana arbitr\303\241ria.JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A Tabela 13 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie da caixa 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. H\303\241 seis superf\303\255cies a serem consideradas, e o fundamental comando SurfaceInt coloca em pares asfaces paralelos da caixa, portanto, apenas tr\303\252s integrais separadas aparecem.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma caixa Integral de superf\303\255cie em uma Caixa em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiYtSSNtbkdGJDYlUSIzRidGNUY3L0YzUSV0cnVlRidGNS9GOFEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGNw== IntegrandoLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiktRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RkAtRiw2JlEiekYnRi9GMkY1RjJGREYyRkQtRkE2LlEiPUYnRjJGREZGL0ZJRjRGSkZMRk5GUEZSL0ZVUSwwLjI3Nzc3NzhlbUYnL0ZYRl9vRjJGRA== use DocumentTools in Do(%MathContainer185 = NULL); end use; use DocumentTools in Do(%MathContainer186 = NULL); Do(%MathContainer187 = NULL); Do(%MathContainer188 = NULL); Do(%MathContainer189 = NULL); Do(%MathContainer190 = NULL); Do(%MathContainer191 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUtSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGK0YvRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRS1JJW1zdWJHRiQ2JS1JI21pR0YkNiZRInhGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JVEiMkYnRi9GMkZPRi9GUi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi9GMg==use DocumentTools in Do(%MathContainer186 = NULL); end use; use DocumentTools in Do(%MathContainer187 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUtSSNtaUdGJDYmUSJ5RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGK0YvRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRS1JJW1zdWJHRiQ2JS1JI21pR0YkNiZRInlGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JVEiMkYnRi9GMkZPRi9GUi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi9GMg==use DocumentTools in Do(%MathContainer188 = NULL); end use; use DocumentTools in Do(%MathContainer189 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUtSSNtaUdGJDYmUSJ6RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGK0YvRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRS1JJW1zdWJHRiQ2JS1JI21pR0YkNiZRInpGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JVEiMkYnRi9GMkZPRi9GUi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi9GMg==use DocumentTools in Do(%MathContainer190 = NULL); end use; use DocumentTools in Do(%MathContainer191 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Fxyz, q, x1,x2,y1,y2,z1,z2; Do(Fxyz = %MathContainer185); Do(x1 = %MathContainer186); Do(x2 = %MathContainer187); Do(y1 = %MathContainer188); Do(y2 = %MathContainer189); Do(z1 = %MathContainer190); Do(z2 = %MathContainer191); if nops([Fxyz])*nops([x1])*nops([x2])*nops([y1])*nops([y2])*nops([z1])*nops([z2])=0 then return;end if; q := SurfaceInt(Fxyz,[x,y,z]=Box(x1..x2,y1..y2,z1..z2),inert); Do(%MathContainer192 = q); Do(%MathContainer193 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer192); if nops([q]) = 0 then return;end if; Do(%MathContainer192 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q; Do(q = %MathContainer192); if nops([q])=0 then return;end if; Do(%MathContainer193 = NULL); Do(%MathContainer193 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer193); if nops([q])=0 then return;end if; Do(%MathContainer193 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer192); Do(q2 = %MathContainer193); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer193 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer193 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer193 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer185 = NULL); Do(%MathContainer186 = NULL); Do(%MathContainer187 = NULL); Do(%MathContainer188 = NULL); Do(%MathContainer189 = NULL); Do(%MathContainer190 = NULL); Do(%MathContainer191 = NULL); Do(%MathContainer192 = NULL); Do(%MathContainer193 = NULL); end use; Tabela 13 Integral de superf\303\255cie de um campo escalar sobre a superf\303\255cie de uma caixa LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 14 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiktRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RkAtRiw2JlEiekYnRi9GMkY1RjJGREYyRkQtRkE2LlEiPUYnRjJGREZGL0ZJRjRGSkZMRk5GUEZSL0ZVUSwwLjI3Nzc3NzhlbUYnL0ZYRl9vRj0tRkE2LlEifkYnRjJGREZGRl1vRkpGTEZORlBGUkZUL0ZYRlYtRkE2LlEiK0YnRjJGREZGRl1vRkpGTEZORlBGUi9GVVEsMC4yMjIyMjIyZW1GJy9GWEZpb0ZaRmVvRmduRjJGRA== sobre a superf\303\255cie da esfera, com raio 3 e centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNiktSSNtbkdGJDYlUSIxRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY6RjBGNEY3RjRGN0Y0Rjc=. O comando SurfaceInt automaticamente escreve a integral em coordenadas esf\303\251ricas, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 \303\251 o \303\242ngulo medido abaixo do eixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTkYyRjw=positivo, e LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEoJnRoZXRhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRi4vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn \303\251 o \303\242ngulo medido em torno desse eixo. Note-se que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEmJnJobztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y0LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMkYnRjVGN0Y1RjcvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiZRJHNpbkYnRjJGNUY3LUkobWZlbmNlZEdGJDYlLUYjNiUtRi82JlEmJnBoaTtGJ0YyRjVGN0Y1RjdGNUY3RjVGNw==, o elemento de \303\241rea de superf\303\255cie em coordenadas esf\303\251ricas, \303\251 automaticamente inserida no integrando.JSFH JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Esfera 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 use DocumentTools in Do(%MathContainer194 = NULL); end use; Raio da Esfera: use DocumentTools in Do(%MathContainer195 = NULL); end use; Centro da Esfera:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer196 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer197 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer198 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Fxyz, q, X,Y,R,Z; Do(Fxyz = %MathContainer194); Do(R = %MathContainer195); Do(X = %MathContainer196); Do(Y = %MathContainer198); Do(Z = %MathContainer197); if nops([Fxyz])*nops([R])*nops([X])*nops([Y])*nops([Z])=0 then return;end if; q := SurfaceInt(Fxyz,[x,y,z]=Sphere(<X,Y,Z>, R),inert); Do(%MathContainer199 = q); Do(%MathContainer200 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer199); if nops([q]) = 0 then return;end if; Do(%MathContainer199 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q; Do(q = %MathContainer199); if nops([q])=0 then return;end if; Do(%MathContainer200 = NULL); Do(%MathContainer200 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer200); if nops([q]) = 0 then return;end if; Do(%MathContainer200 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer199); Do(q2 = %MathContainer200); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer200 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer200 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer200 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer194 = NULL); Do(%MathContainer195 = NULL); Do(%MathContainer196 = NULL); Do(%MathContainer197 = NULL); Do(%MathContainer198 = NULL); Do(%MathContainer199 = NULL); Do(%MathContainer200 = NULL); end use; Tabela 14 Integral de superf\303\255cie de um campo escalar sobre a superf\303\255cie de uma esfera LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 15 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJ4RidGL0YyRjUtRjk2LlEifkYnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRlgtRiw2JlEieUYnRi9GMkY1RjJGPA== cujo dom\303\255nio \303\251 a regi\303\243o plana limitada pelas curvas 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 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GIzYmLUYsNiNRIUYnLUkmbXNxcnRHRiQ2Iy1GIzYlLUYsNiZRInhGJ0YvRjJGNUYyRjxGMkY8RlNGMkY8. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida Parametricamente 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 use DocumentTools in Do(%MathContainer201 = NULL); end use; 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 use DocumentTools in Do(%MathContainer202 = NULL); 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end use; 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use DocumentTools in Do(%Label133(caption) = h(u)); Do(%Label134(caption) = g(u)); end use; 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSI9RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGNS8lKnNlcGFyYXRvckdGNS8lKXN0cmV0Y2h5R0Y1LyUqc3ltbWV0cmljR0Y1LyUobGFyZ2VvcEdGNS8lLm1vdmFibGVsaW1pdHNHRjUvJSdhY2NlbnRHRjUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJRjNGNg==use DocumentTools in Do(%MathContainer205 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer206 = NULL); end use; use DocumentTools in Do(%Label133(caption) = H(v)); Do(%Label134(caption) = G(v)); end use; 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSI9RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGNS8lKnNlcGFyYXRvckdGNS8lKXN0cmV0Y2h5R0Y1LyUqc3ltbWV0cmljR0Y1LyUobGFyZ2VvcEdGNS8lLm1vdmFibGVsaW1pdHNHRjUvJSdhY2NlbnRHRjUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLyUnaXRhbGljR1EldHJ1ZUYnRjMvRjdRJ2l0YWxpY0Ynuse DocumentTools in Do(%MathContainer207 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYvRjJGNQ==use DocumentTools in Do(%MathContainer208 = NULL); end use; JSFHJSFH use DocumentTools,VectorCalculus in module() local Fxyz, q, X,Y,Z,A,B,a,b; Do(Fxyz = %MathContainer201); Do(X = %MathContainer202); Do(Y = %MathContainer203); Do(Z = %MathContainer204); Do(B = %MathContainer205); Do(A = %MathContainer207); Do(b = %MathContainer206); Do(a = %MathContainer208); if nops([Fxyz])*nops([X])*nops([Y])*nops([Z])*nops([A])*nops([B])*nops([a])*nops([b])=0 then return;end if; if Do(%RadioButton19) then q := SurfaceInt(Fxyz,[x,y,z]=Surface(<X,Y,Z>, u=a..b,v=A..B),inert); else q := SurfaceInt(Fxyz,[x,y,z]=Surface(<x,y,Z>, v=a..b,u=A..B),inert); end if; Do(%MathContainer209 = q); Do(%MathContainer210 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer209); if nops([q]) = 0 then return;end if; Do(%MathContainer209 = simplify(q)); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local q; Do(q = %MathContainer209); if nops([q]) = 0 then return;end if; Do(%MathContainer210 = NULL); Do(%MathContainer210 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer210); if nops([q]) = 0 then return;end if; Do(%MathContainer210 = simplify(q)); end module; end use; JSFH use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer209); Do(q2 = %MathContainer210); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer210 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer210 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer210 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer201 = NULL); Do(%MathContainer202 = NULL); Do(%MathContainer203 = NULL); Do(%MathContainer204 = NULL); Do(%MathContainer205 = NULL); Do(%MathContainer207 = NULL); Do(%MathContainer206 = NULL); Do(%MathContainer208 = NULL); Do(%RadioButton19(value)=true); Do(%Label133(caption) = h(u)); Do(%Label134(caption) = g(u)); Do(%MathContainer209 = NULL); Do(%MathContainer210 = NULL); end use; Tabela 15 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida parametricamente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Note o elemento da \303\241rea de superf\303\255cie 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 no integrando. Devido a isso, o Maple pode avaliar a integral interior analiticamente, mas a resultante integral externa deve ser avaliada numericamente. Integrais de superf\303\255cie s\303\243o algumas das integrais mais dif\303\255ceis no c\303\241lculo para avaliar de forma fechada. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 16 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie 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 cujo dom\303\255nio \303\251 o ret\303\242ngulo 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. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida sobre um Ret\303\242ngulo 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 use DocumentTools in Do(%MathContainer211 = NULL); end use; use DocumentTools in Do(%MathContainer213 = NULL); Do(%MathContainer215 = NULL); Do(%MathContainer214 = NULL); Do(%MathContainer216 = NULL); end use; Superf\303\255cie Ret\303\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 use DocumentTools in Do(%MathContainer212 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer213 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer214 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer215 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer216 = NULL); end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local Fxyz, q, x1,x2,y1,y2,Z; Do(Fxyz = %MathContainer211); Do(x2 = %MathContainer213); Do(x1 = %MathContainer215); Do(y2 = %MathContainer214); Do(y1 = %MathContainer216); Do(Z = %MathContainer212); if nops([Fxyz])*nops([x1])*nops([x2])*nops([y1])*nops([y2])*nops([Z])=0 then return;end if; q := SurfaceInt(Fxyz,[x,y,z]=Surface(<x,y,Z>, [x,y]=Rectangle(x1..x2,y1..y2)),inert); Do(%MathContainer217 = q); Do(%MathContainer218 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer217); if nops([q]) = 0 then return;end if; Do(%MathContainer217 = simplify(q)); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local q; Do(q = %MathContainer217); if nops([q])=0 then return;end if; Do(%MathContainer218 = NULL); Do(%MathContainer218 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer218); if nops([q]) = 0 then return;end if; Do(%MathContainer218 = simplify(q)); end module; end use; JSFH use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer217); Do(q2 = %MathContainer218); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer218 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer218 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer218 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer211 = NULL); Do(%MathContainer213 = NULL); Do(%MathContainer215 = NULL); Do(%MathContainer214 = NULL); Do(%MathContainer216 = NULL); Do(%MathContainer217 = NULL); Do(%MathContainer218 = NULL); Do(%MathContainer212 = NULL); end use; Tabela 16 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida sobre um ret\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Note o elemento da \303\241rea de superf\303\255cie 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 no integrando. Devido a isso, o Maple pode avaliar a integral interior analiticamente, mas a resultante integral externa deve ser avaliada numericamente. Integrais de superf\303\255cie s\303\243o algumas das integrais mais dif\303\255ceis no c\303\241lculo para avaliar de forma fechada. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 17 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie 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 cujo dom\303\255nio \303\251 o disco com o centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIxRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMkYnRjRGN0Y0RjdGNEY3RjRGNw== e raio 3. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida sobre um Disco 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 use DocumentTools in Do(%MathContainer219 = NULL); end use; Superf\303\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 use DocumentTools in Do(%MathContainer220 = NULL); end use; Centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNictSSNtaUdGJDYnUSJoRicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIixGJ0Y0RjovRj5RJ25vcm1hbEYnLyUmZmVuY2VHRjwvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGPC8lKnN5bW1ldHJpY0dGPC8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y8LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2J1Eia0YnRjRGN0Y6Rj1GOkZERjRGOkZERjpGRA==:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer221 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer222 = NULL); end use; Raio:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYvRjJGNQ==use DocumentTools in Do(%MathContainer223 = NULL); end use; use DocumentTools in Do(%MathContainer226 = NULL); Do(%MathContainer227 = NULL); Do(%MathContainer224 = 0); Do(%MathContainer225 = 2*Pi); end use; use DocumentTools in Do(%MathContainer226 = NULL); Do(%MathContainer227 = NULL); Do(%MathContainer224 = NULL); Do(%MathContainer225 = NULL); end use; From LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= use DocumentTools in Do(%MathContainer224 = NULL); Do(%MathContainer225 = NULL); end use; JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Fxyz, q, X,Y,R,Z, T1,T2; Do(Fxyz = %MathContainer219); Do(Z = %MathContainer220); Do(X = %MathContainer221); Do(Y = %MathContainer222); Do(R = %MathContainer223); Do(T1 = %MathContainer224); Do(T2 = %MathContainer225); if nops([Fxyz])*nops([Z])*nops([X])*nops([Y])*nops([R])*nops([T1])*nops([T2])=0 then return;end if; if Do(%RadioButton21) then q:=SurfaceInt(Fxyz, [x,y,z]=Surface(<x,y,Z>, [x,y]=Circle(<X,Y>,R,[r,theta])),inert); else q := SurfaceInt(Fxyz, [x,y,z]=Surface(<x,y,Z>, [x,y]=Sector(Circle(<X,Y>,R,[r,theta]),T1,T2)),inert); end if; Do(%MathContainer226 = q); Do(%MathContainer227 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer226); if nops([q]) = 0 then return;end if; Do(%MathContainer226 = simplify(q)); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local q; Do(q = %MathContainer226); if nops([q]) = 0 then return;end if; Do(%MathContainer227 = NULL); Do(%MathContainer227 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer227); if nops([q]) = 0 then return;end if; Do(%MathContainer227 = simplify(q)); end module; end use; JSFH use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer226); Do(q2 = %MathContainer227); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer227 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer227 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer227 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer219 = NULL); Do(%MathContainer220 = NULL); Do(%MathContainer221 = NULL); Do(%MathContainer222 = NULL); Do(%MathContainer223 = NULL); Do(%MathContainer226 = NULL); Do(%MathContainer227 = NULL); Do(%RadioButton21 = true); Do(%MathContainer224 = 0); Do(%MathContainer225 = 2*Pi); end use; Tabela 17 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida sobre um disco LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Maple gasta pelo menos cinco minutos tentando avaliar essa integral de forma fechada, mas nunca consegue. O c\303\241lculo foi interrompido pressionando o \303\255cone de interrup\303\247\303\243o (sinal hexagonal com a m\303\243o sobreposta) na barra de ferramentas. A aproxima\303\247\303\243o num\303\251rica da integral foi obtida pressionando o bot\303\243o Floating-Point Approximation. Como j\303\241 foi mencionado anteriormente, integrais de superf\303\255cie s\303\243o alguns dos mais dif\303\255ceis integrais no c\303\241lculo para avaliar de forma fechada. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 18 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJ4RidGL0YyRjUtRjk2LlEifkYnRjJGPEY+RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRlgtRiw2JlEieUYnRi9GMkY1RjJGPA== cujo dom\303\255nio \303\251 o interior da elipse 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. Tal como acontece com o c\303\241lculo de fluxo, os par\303\242metros de superf\303\255cie s\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn, mas na integral SurfaceInt, as coordenadas s\303\243o automaticamente alteradas para polares para acomodar o dom\303\255nio da superf\303\255cie. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida sobre uma Elipse 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 use DocumentTools in Do(%MathContainer228 = NULL); end use; Superf\303\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 use DocumentTools in Do(%MathContainer229 = NULL); end use; Equa\303\247\303\243o da Elipse: use DocumentTools in Do(%MathContainer230 = NULL); end use; use DocumentTools in Do(%MathContainer234 = NULL); Do(%MathContainer235 = NULL); Do(%MathContainer231 = 0); Do(%MathContainer232 = 2*Pi); end use; use DocumentTools in Do(%MathContainer234 = NULL); Do(%MathContainer235 = NULL); Do(%MathContainer231 = NULL); Do(%MathContainer232 = NULL); end use; From LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= use DocumentTools in Do(%MathContainer231 = NULL); Do(%MathContainer232 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local Fxyz, q,q1,Eq, X,Z, T1,T2; Do(Fxyz = %MathContainer228); Do(Z = %MathContainer229); Do(q1 = %MathContainer230); Do(T1 = %MathContainer231); Do(T2 = %MathContainer232); if type(q1,`=`) then Eq:=lhs(q1)-rhs(q1) else Eq:=q1;end if; if nops([Fxyz])*nops([Z])*nops([Eq])*nops([T1])*nops([T2])=0 then return;end if; if Do(%RadioButton23) then q:=SurfaceInt(Fxyz, [x,y,z]=Surface(<x,y,Z>, [x,y]=Ellipse(Eq,[r,theta])),inert); else q := SurfaceInt(Fxyz, [x,y,z]=Surface(<x,y,Z>, [x,y]=Sector(Ellipse(Eq,[r,theta]),T1,T2)),inert); end if; Do(%MathContainer234 = q); Do(%MathContainer235 = NULL); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEjZHJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEiZEYnRi9GMkY1LUYsNiZRJyYjOTUyO0YnL0YwRjRGMkY8RjJGPA== use DocumentTools in module() local q; Do(q = %MathContainer234); if nops([q]) = 0 then return;end if; Do(%MathContainer234 = simplify(q)); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local q; Do(q = %MathContainer234); if nops([q]) = 0 then return;end if; Do(%MathContainer235 = NULL); Do(%MathContainer235 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer235); if nops([q]) = 0 then return;end if; Do(%MathContainer235 = simplify(q)); end module; end use; JSFH use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer234); Do(q2 = %MathContainer235); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer235 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer235 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer235 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer228 = NULL); Do(%MathContainer229 = NULL); Do(%MathContainer230 = NULL); Do(%MathContainer234 = NULL); Do(%MathContainer235 = NULL); Do(%RadioButton23 = true); Do(%MathContainer231 = 0); Do(%MathContainer232 = 2*Pi); Do(%MathContainer233 = NULL); end use; Tabela 18 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida sobre o interior de uma elipse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A integral interior pode ser avaliada analiticamente, mas a resultante integral externa s\303\263 pode ser avaliada numericamente. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 19 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da uma fun\303\247\303\243o escalar 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 sobre a superf\303\255cie 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 cujo dom\303\255nio \303\251 o interior do tri\303\242ngulo com v\303\251rtices 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.JSFH JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida sobre um Tri\303\242ngulo 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 use DocumentTools in Do(%MathContainer236 = NULL); end use; Superf\303\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 use DocumentTools in Do(%MathContainer237 = NULL); end use; V\303\251rtices do Tri\303\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use DocumentTools in Do(%MathContainer238 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer239 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer240 = NULL); end use; use DocumentTools in Do(%MathContainer238 = NULL); Do(%MathContainer241 = NULL); Do(%MathContainer239 = NULL); Do(%MathContainer242 = NULL); Do(%MathContainer240 = NULL); Do(%MathContainer243 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer241 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer242 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer243 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Fxyz, q, Z, x1,y1,x2,y2,x3,y3; Do(Fxyz = %MathContainer236); Do(Z = %MathContainer237); Do(x1 = %MathContainer238); Do(y1 = %MathContainer241); Do(x2 = %MathContainer239); Do(y2 = %MathContainer242); Do(x3 = %MathContainer240); Do(y3 = %MathContainer243); if nops([Fxyz])*nops([Z])*nops([x1])*nops([y1])*nops([x2])*nops([y2])*nops([x3])*nops([y3])=0 then return;end if; q := SurfaceInt(Fxyz,[x,y,z]=Surface(<x,y,Z>, [x,y]=Triangle(<x1,y1>,<x2,y2>,<x3,y3>)),inert); Do(%MathContainer244 = q); Do(%MathContainer245 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer244); if nops([q]) = 0 then return;end if; Do(%MathContainer244 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q; Do(q = %MathContainer244); if nops([q]) = 0 then return;end if; Do(%MathContainer245 = NULL); Do(%MathContainer245 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer245); if nops([q]) = 0 then return;end if; Do(%MathContainer245 = simplify(q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer244); Do(q2 = %MathContainer245); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer245 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer245 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer245 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer236 = NULL); Do(%MathContainer237 = NULL); Do(%MathContainer238 = NULL); Do(%MathContainer241 = NULL); Do(%MathContainer239 = NULL); Do(%MathContainer242 = NULL); Do(%MathContainer240 = NULL); Do(%MathContainer243 = NULL); Do(%MathContainer244 = NULL); Do(%MathContainer245 = NULL); end use; Table 19 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida sobre o interior de um tri\303\242ngulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= As integrais internas podem ser avaliadas exatamente, as integrais exteriores resultantes s\303\263 podem ser avaliadas numericamente. O fundamental comando SurfaceInt escreve a integral como uma soma porque o dom\303\255nio triangular n\303\243o pode ser varrido com uma \303\272nica integral m\303\272ltipla. A partir dos limites de integra\303\247\303\243o nas integrais exibidas, seria poss\303\255vel deduzir as equa\303\247\303\265es para as retas que comp\303\265em os lados do tri\303\242ngulo. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH Tabela 20 cont\303\251m um modelo de tarefa utilizada para calcular a integral de superf\303\255cie da fun\303\247\303\243o escalar 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 sobre a superf\303\255cie 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 cujo dom\303\255nio \303\251 a regi\303\243o do primeiro quadrante limitado pelas curvas 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. O modelo de tarefa oferece a op\303\247\303\243o para integrar em qualquer ordem, isto \303\251, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHhGJ0YvRjJGNUYyRjw=, or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHlGJ0YvRjJGNUYyRjw=. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o de Superf\303\255cie\342\211\273Sobre uma Caixa Integral de Superf\303\255cie sobre uma Superf\303\255cie Definida sobre uma Regi\303\243o 2-D Geral 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 use DocumentTools in Do(%MathContainer246 = NULL); end use; Superf\303\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 use DocumentTools in Do(%MathContainer247 = NULL); 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Do(%Label136(caption) = u(y)); end use; 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSI9RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGNS8lKnNlcGFyYXRvckdGNS8lKXN0cmV0Y2h5R0Y1LyUqc3ltbWV0cmljR0Y1LyUobGFyZ2VvcEdGNS8lLm1vdmFibGVsaW1pdHNHRjUvJSdhY2NlbnRHRjUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJRjNGNg==use DocumentTools in Do(%MathContainer248 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer249 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSNtb0dGJDYuUSI9RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGNS8lKnNlcGFyYXRvckdGNS8lKXN0cmV0Y2h5R0Y1LyUqc3ltbWV0cmljR0Y1LyUobGFyZ2VvcEdGNS8lLm1vdmFibGVsaW1pdHNHRjUvJSdhY2NlbnRHRjUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZJLyUnaXRhbGljR1EldHJ1ZUYnRjMvRjdRJ2l0YWxpY0Ynuse DocumentTools in Do(%MathContainer250 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYvRjJGNQ==use DocumentTools in Do(%MathContainer251 = NULL); end use; JSFHJSFH use DocumentTools,VectorCalculus in module() local Fxyz, q, u,v,a,b,Z; Do(Fxyz = %MathContainer246); Do(Z = %MathContainer247); Do(v = %MathContainer248); Do(u = %MathContainer250); Do(b = %MathContainer249); Do(a = %MathContainer251); if nops([Fxyz])*nops([Z])*nops([v])*nops([u])*nops([b])*nops([a])=0 then return;end if; if Do(%RadioButton25) then q := SurfaceInt(Fxyz,[x,y,z]=Surface(<x,y,Z>, x=a..b,y=u..v),inert); else q := SurfaceInt(Fxyz,[x,y,z]=Surface(<x,y,Z>, y=a..b,x=u..v),inert); end if; Do(%MathContainer252 = q); Do(%MathContainer253 = NULL); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer252); if nops([q]) = 0 then return;end if; Do(%MathContainer252 = simplify(q)); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local q; Do(q = %MathContainer252); if nops([q]) = 0 then return;end if; Do(%MathContainer253 = NULL); Do(%MathContainer253 = value(q)); end module; end use; use DocumentTools in module() local q; Do(q = %MathContainer253); if nops([q]) = 0 then return;end if; Do(%MathContainer253 = simplify(q)); end module; end use; JSFH use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer252); Do(q2 = %MathContainer253); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer253 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer253 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer253 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer246 = NULL); Do(%MathContainer247 = NULL); Do(%MathContainer248 = NULL); Do(%MathContainer250 = NULL); Do(%MathContainer249 = NULL); Do(%MathContainer251 = NULL); Do(%RadioButton25(value)=true); Do(%Label135(caption) = v(x)); Do(%Label136(caption) = u(x)); Do(%MathContainer252 = NULL); Do(%MathContainer253 = NULL); end use; Tabela 20 Integral de superf\303\255cie de um campo escalar sobre uma superf\303\255cie definida sobre uma regi\303\243o plana geral LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A integral interior pode ser avaliada exatamente, mas a integral externa resultante s\303\263 pode ser avaliada numericamente. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH Nos pacotes VectorCalculus, o comando int foi modificado com a sintaxe especial para tornar a escrita de integrais m\303\272ltiplas mais f\303\241cil. Assim, a integral iterada 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 JSFH pode ser constru\303\255da em alto n\303\255vel com um dos comandos mostrados na Tabela 36. 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

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtRiM2JC1JImZHRic2JEkieEdGJ0kieUdGJy9GLjtJImFHRidJImJHRicvRi87SSJjR0YnSSJkR0Yn

JSFH 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

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtSSJmR0YnNiRJInhHRidJInlHRic3JC9GLDtJImFHRidJImJHRicvRi07SSJjR0YnSSJkR0Yn

JSFH Tabela 21 Maneiras de alto n\303\255vel para escrever uma integral dupla iterada JSFH Integra\303\247\303\243o feita com a sintaxe, \303\240 direita na Tabela 21 \303\251 mais robusta que aquele do lado esquerdo. Correspondente ao uso mais velho \303\240 esquerda da Tabela 21, temos a especial sintaxe VectorCalculus 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

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtRiM2JC1JImZHRic2JEkieEdGJ0kieUdGJy9GLjtJImFHRidJImJHRicvRi87SSJjR0YnSSJkR0Yn

JSFH A integral inerte \303\251 gerada adicionando o par\303\242metro opcional "inerte" para o comando int modificado. Al\303\251m disso, os dom\303\255nios especiais do ret\303\242ngulo, disco, elipse e tri\303\242ngulo s\303\243o reconhecidos, junto com disposi\303\247\303\243o para a formula\303\247\303\243o de uma integral dupla sobre uma regi\303\243o planar geral. Estas integra\303\247\303\265es s\303\243o implementadas nos seguintes modelos de tarefa.

JSFH Tabela 22 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre o ret\303\242ngulo 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.JSFH JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2732-D\342\211\273Sobre um Ret\303\242ngulo Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RjJGREYyRkRGMkZE sobre um Ret\303\242ngulo 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 use DocumentTools in Do(%MathContainer254 = NULL); end use; Integral Interior: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUtSSNtaUdGJDYmUSJ4RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGK0YvRjI= use DocumentTools in Do(%MathContainer255 = NULL); Do(%MathContainer256 = NULL); end use; Integral Exterior: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUtSSNtaUdGJDYmUSJ5RicvJSdpdGFsaWNHUSV0cnVlRidGLy9GM1EnaXRhbGljRidGK0YvRjI= use DocumentTools in Do(%MathContainer257 = NULL); Do(%MathContainer258 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local f, a,b,c,d, q; Do(f = %MathContainer254); Do(a = %MathContainer255); Do(b = %MathContainer256); Do(c = %MathContainer257); Do(d = %MathContainer258); if nops([f])*nops([a])*nops([b])*nops([c])*nops([d])=0 then return;end if; if has(a,{x,y}) or has(b,{x,y}) or has(c,{x,y}) or has(d,{x,y}) then return; end if; q := int(f,[x,y]=Rectangle(a..b,c..d),inert); Do(%MathContainer259 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHlGJ0YvRjJGNUYyRjw= JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer259); if nops([Q])=0 then return;end if; Do(%MathContainer260 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer260); if nops([q])=0 then return;end if; Do(%MathContainer260 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer259); Do(q2 = %MathContainer260); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer260 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer260 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer260 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer254 = NULL); Do(%MathContainer255 = NULL); Do(%MathContainer256 = NULL); Do(%MathContainer257 = NULL); Do(%MathContainer259 = NULL); Do(%MathContainer260 = NULL); Do(%MathContainer258 = NULL); end use; Tabela 22 Integral dupla Iterada sobre um dom\303\255nio retangular JSFHJSFH

JSFH Tabela 23 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre um disco com centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIxRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMkYnRjRGN0Y0RjdGNEY3RjRGNw== e raio 3.JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2732-D\342\211\273Sobre um C\303\255rculo Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn sobre um C\303\255rculo 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 use DocumentTools in Do(%MathContainer261 = NULL); end use; Centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYlLUYjNictSSNtaUdGJDYmUSJoRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSIsRidGNy9GO1Enbm9ybWFsRicvJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYmUSJrRidGNEY3RjpGN0ZBRjdGQS1GMTYjUSFGJ0Y3RkE=: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw= use DocumentTools in Do(%MathContainer262 = NULL); Do(%MathContainer263 = NULL); end use; Raio = use DocumentTools in Do(%MathContainer264 = NULL); end use; use DocumentTools in Do(%MathContainer267 = NULL); Do(%MathContainer268 = NULL); Do(%MathContainer265 = 0); Do(%MathContainer266 = 2*Pi); end use; use DocumentTools in Do(%MathContainer267 = NULL); Do(%MathContainer268 = NULL); Do(%MathContainer265 = NULL); Do(%MathContainer266 = NULL); end use; From LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= use DocumentTools in Do(%MathContainer265 = NULL); Do(%MathContainer266 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local f, h,k, R, q, T1, T2, C; Do(f = %MathContainer261); Do(h = %MathContainer262); Do(k = %MathContainer263); Do(R = %MathContainer264); Do(T1 = %MathContainer265); Do(T2 = %MathContainer266); if nops([f])*nops([h])*nops([k])*nops([R])*nops([T1])*nops([T2])=0 then return;end if; C := Vector([h,k],coords=cartesian[x,y]); if Do(%RadioButton27) then q := int(f,[x,y]=Circle(C,R,[r,theta]),inert); else q := int(f,[x,y]=Sector(Circle(C,R,[r,theta]),T1,T2),inert); end if; Do(%MathContainer267 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRJyYjOTUyO0YnL0YwRjRGMi9GNlEnbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY8LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUi1GLDYmUSNkckYnRi9GMkY1RjJGPA== JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer267); if nops([Q])=0 then return;end if; Do(%MathContainer268 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer268); if nops([q])=0 then return;end if; Do(%MathContainer268 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer267); Do(q2 = %MathContainer268); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer268 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer268 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer268 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer261 = NULL); Do(%MathContainer262 = NULL); Do(%MathContainer263 = NULL); Do(%MathContainer264 = NULL); Do(%MathContainer267 = NULL); Do(%MathContainer268 = NULL); Do(%RadioButton27 = true); Do(%MathContainer265 = 0); Do(%MathContainer266 = 2*Pi); end use; Tabela 23 Integral dupla iterada sobre o disco com centro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIxRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMkYnRjRGN0Y0RjdGNEY3RjRGNw== e raio 3 JSFH

JSFH Tabela 24 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre o interior da elipse 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. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2732-D\342\211\273Sobre uma Elipse Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RjJGREYyRkRGMkZE sobre uma Elipse 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 use DocumentTools in Do(%MathContainer269 = NULL); end use; Equa\303\247\303\243o da elipse: use DocumentTools in Do(%MathContainer270 = NULL); end use; use DocumentTools in Do(%MathContainer274 = NULL); Do(%MathContainer275 = NULL); Do(%MathContainer271 = 0); Do(%MathContainer272 = 2*Pi); Do(%MathContainer273 = NULL); end use; use DocumentTools in Do(%MathContainer274 = NULL); Do(%MathContainer275 = NULL); Do(%MathContainer271 = NULL); Do(%MathContainer272 = NULL); Do(%MathContainer273 = NULL); end use; De LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI9RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGS0YyRjQ= use DocumentTools in Do(%MathContainer271 = NULL); Do(%MathContainer272 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local f, q, q1, Eq, T1, T2; Do(f = %MathContainer269); Do(q1 = %MathContainer270); Do(T1 = %MathContainer271); Do(T2 = %MathContainer272); if type(q1,`=`) then Eq:=lhs(q1)-rhs(q1) else Eq:=q1;end if; if nops([f])*nops([Eq])*nops([T1])*nops([T2])=0 then return;end if; if Do(%RadioButton29) then q := int(f,[x,y]=Ellipse(Eq,[r,theta]),inert); #Do(%MathContainer273 = dy*dx); else q := int(f,[x,y]=Sector(Ellipse(Eq,[r,theta]),T1,T2),inert); end if; SetProperty(MathContainer273, value, "<math><mrow><mi>dr</mi><mspace width='0.3em'/><mi>d</mi><mi mathvariant='normal'>&theta;</mi ></mrow></math>"); Do(%MathContainer274 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer274); if nops([Q])=0 then return;end if; Do(%MathContainer275 = value(Q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=use DocumentTools in module() local q; Do(q = %MathContainer275); if nops([q])=0 then return;end if; Do(%MathContainer275 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer274); Do(q2 = %MathContainer275); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer275 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer275 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer275 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer269 = NULL); Do(%MathContainer270 = NULL); Do(%MathContainer274 = NULL); Do(%MathContainer275 = NULL); Do(%RadioButton29 = true); Do(%MathContainer271 = 0); Do(%MathContainer272 = 2*Pi); Do(%MathContainer273 = NULL); end use; Tabela 24 Integral dupla iterada sobre um dom\303\255nio el\303\255ptico JSFH

JSFH Tabela 25 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre o interior do tri\303\242ngulo cujos v\303\251rtices s\303\243o 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. JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2732-D\342\211\273Sobre um Ret\303\242ngulo Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RjJGREYyRkRGMkZE sobre um Tri\303\242ngulo 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 use DocumentTools in Do(%MathContainer276 = NULL); end use; V\303\251rticesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer277 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer278 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer279 = NULL); end use; use DocumentTools in Do(%MathContainer277 = NULL); Do(%MathContainer280 = NULL); Do(%MathContainer278 = NULL); Do(%MathContainer281 = NULL); Do(%MathContainer279 = NULL); Do(%MathContainer282 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer280 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer281 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer282 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local f, q, x1,x2,x3,y1,y2,y3; Do(f = %MathContainer276); Do(x1 = %MathContainer277); Do(y1 = %MathContainer280); Do(x2 = %MathContainer278); Do(y2 = %MathContainer281); Do(x3 = %MathContainer279); Do(y3 = %MathContainer282); if nops([f])*nops([x1])*nops([x2])*nops([x3])*nops([y1])*nops([y2])*nops([y3])=0 then return;end if; q := int(f,[x,y]=Triangle(<x1,y1>,<x2,y2>,<x3,y3>),inert); Do(%MathContainer283 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHhGJ0YvRjJGNUYyRjw= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer283); if nops([Q])=0 then return;end if; Do(%MathContainer284 = value(Q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=use DocumentTools in module() local q; Do(q = %MathContainer284); if nops([q])=0 then return;end if; Do(%MathContainer284 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer283); Do(q2 = %MathContainer284); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer284 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer284 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer284 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer276 = NULL); Do(%MathContainer277 = NULL); Do(%MathContainer280 = NULL); Do(%MathContainer278 = NULL); Do(%MathContainer281 = NULL); Do(%MathContainer279 = NULL); Do(%MathContainer282 = NULL); Do(%MathContainer283 = NULL); Do(%MathContainer284 = NULL); end use; Tabela 25 Integral dupla iterada sobre o interior de um tri\303\242ngulo JSFH

JSFH Tabela 26 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre a parcela do primeiro quadrante limitado pelas curvas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GIzYmLUYsNiNRIUYnLUkmbXNxcnRHRiQ2Iy1GIzYlLUYsNiZRInhGJ0YvRjJGNUYyRjxGMkY8RlNGMkY8 e 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.JSFH JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2732-D\342\211\273Sobre um Ret\303\242ngulo Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RjJGREYyRkRGMkZE sobre uma Regi\303\243o Geral 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 use DocumentTools in Do(%MathContainer285 = NULL); end use; 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use DocumentTools in Do(%MathContainer286 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=use DocumentTools in Do(%MathContainer287 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiYtRiw2JlEieEYnRi9GMkY1Ri9GMkY1RjIvRjZRJ25vcm1hbEYnLUkjbW9HRiQ2LlEiPUYnRjJGQC8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGL0YyRjU=use DocumentTools in Do(%MathContainer288 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYvRjJGNQ==use DocumentTools in Do(%MathContainer289 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local f, q, a,b,u,v; Do(f = %MathContainer285); Do(v = %MathContainer286); Do(u = %MathContainer288); Do(b = %MathContainer287); Do(a = %MathContainer289); if nops([f])*nops([a])*nops([b])*nops([u])*nops([v])=0 then return;end if; q := int(f,[x,y]=Region(a..b,u..v),inert); Do(%MathContainer290 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEjZHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHhGJ0YvRjJGNUYyRjw= JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer290); if nops([Q])=0 then return;end if; Do(%MathContainer291 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer291); if nops([q])=0 then return;end if; Do(%MathContainer291 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer290); Do(q2 = %MathContainer291); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer291 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer291 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer291 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer285 = NULL); Do(%MathContainer286 = NULL); Do(%MathContainer288 = NULL); Do(%MathContainer287 = NULL); Do(%MathContainer289 = NULL); Do(%MathContainer290 = NULL); Do(%MathContainer291 = NULL); end use; Tabela 26 Integral dupla iterada sobre uma regi\303\243o planar, com curvas limitadas JSFH

JSFH Nos pacotes VectorCalculus, o modificado comando int suporta a integra\303\247\303\243o sobre um cubo, esfera, e tetraedro, e sobre uma regi\303\243o tridimensional geral. Os modelos de tarefas a seguir implementam essas integra\303\247\303\265es. JSFH

JSFH Tabela 27 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre o cubo 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.JSFH JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2733-D\342\211\273Sobre um Cubo Integrar 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 sobre um Cubo 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 use DocumentTools in Do(%MathContainer292 = NULL); end use; 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use DocumentTools in Do(%MathContainer2933 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer2934 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer2935 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer2936 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer2937 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer2938 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local f, q, x1,x2,y1,y2,z1,z2; Do(f = %MathContainer292); Do(x2 = %MathContainer293); Do(x1 = %MathContainer296); Do(y2 = %MathContainer294); Do(y1 = %MathContainer297); Do(z2 = %MathContainer295); Do(z1 = %MathContainer298); if nops([f])*nops([x1])*nops([x2])*nops([y1])*nops([y2])*nops([z1])*nops([z2])=0 then return;end if; q := int(f,[x,y,z]=Parallelepiped(x1..x2,y1..y2,z1..z2),inert); Do(%MathContainer299 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHlGJ0YvRjJGNUY4LUYsNiZRI2R6RidGL0YyRjVGMkY8 JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer299); if nops([Q])=0 then return;end if; Do(%MathContainer300 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer300); if nops([q])=0 then return;end if; Do(%MathContainer300 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer299); Do(q2 = %MathContainer300); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer300 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer300 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer300 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer292 = NULL); Do(%MathContainer293 = NULL); Do(%MathContainer296 = NULL); Do(%MathContainer294 = NULL); Do(%MathContainer297 = NULL); Do(%MathContainer295 = NULL); Do(%MathContainer298 = NULL); Do(%MathContainer299 = NULL); Do(%MathContainer300 = NULL); end use; Tabela 27 Integral tripla iterada sobre um cubo em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiYtSSNtbkdGJDYlUSIzRidGNUY3L0YzUSV0cnVlRidGNS9GOFEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGNw== JSFH

JSFH Tabela 28 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre a esfera com o centro 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e raio 4. JSFH Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2733-D\342\211\273Sobre uma Esfera Integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn sobre uma Esfera 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 use DocumentTools in Do(%MathContainer301 = NULL); end use; Centro 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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw=, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTkYyRjw= use DocumentTools in Do(%MathContainer302 = NULL); Do(%MathContainer303 = NULL); Do(%MathContainer304 = NULL); end use; Raio = use DocumentTools in Do(%MathContainer305 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local f, a,b,c, R, q; Do(f = %MathContainer301); Do(a = %MathContainer302); Do(b = %MathContainer303); Do(c = %MathContainer304); Do(R = %MathContainer305); if nops([f])*nops([a])*nops([b])*nops([c])*nops([R])=0 then return;end if; q := int(f,[x,y,z]=Sphere(<a,b,c>,R,[rho,phi,theta]),inert); Do(%MathContainer306 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JlEiZEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYsNiZRJyYjOTUyO0YnL0YwRjRGMi9GNlEnbm9ybWFsRictSSNtb0dGJDYuUSJ+RidGMkY8LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUkYrLUYsNiZRJyYjOTY2O0YnRjtGMkY8Rj5GKy1GLDYmUScmIzk2MTtGJ0Y7RjJGPEYyRjw= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer306); if nops([Q])=0 then return;end if; Do(%MathContainer307 = value(Q)); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=use DocumentTools in module() local q; Do(q = %MathContainer307); if nops([q])=0 then return;end if; Do(%MathContainer307 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer306); Do(q2 = %MathContainer307); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer307 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer307 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer307 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer301 = NULL); Do(%MathContainer302 = NULL); Do(%MathContainer303 = NULL); Do(%MathContainer304 = NULL); Do(%MathContainer305 = NULL); Do(%MathContainer306 = NULL); Do(%MathContainer307 = NULL); end use; Table 28 Integral tripla iterada sobre uma esfera em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiYtSSNtbkdGJDYlUSIzRidGNUY3L0YzUSV0cnVlRidGNS9GOFEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGNw== JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH Tabela 29 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre o interior de um tetraedro com v\303\251rtices 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.JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2733-D\342\211\273Sobre um Cubo Integrar 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 sobre um Tetraedro 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 use DocumentTools in Do(%MathContainer308 = NULL); end use; V\303\251rtices use DocumentTools in Do(%MathContainer309 = NULL); Do(%MathContainer313 = NULL); Do(%MathContainer317 = NULL); Do(%MathContainer310 = NULL); Do(%MathContainer314 = NULL); Do(%MathContainer318 = NULL); Do(%MathContainer311 = NULL); Do(%MathContainer315 = NULL); Do(%MathContainer319 = NULL); Do(%MathContainer312 = NULL); Do(%MathContainer316 = NULL); Do(%MathContainer320 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer309 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer310 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer311 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSI0RidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer312 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer313 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer314 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer315 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSI0RidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer316 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer317 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer318 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIzRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer319 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSI0RidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ== use DocumentTools in Do(%MathContainer320 = NULL); end use; JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= use DocumentTools,VectorCalculus in module() local f, x1,x2,x3,y1,y2,y3,z1,z2,z3, v1,v2,v3,v4, q; Do(f = %MathContainer308); Do(x1 = %MathContainer309); Do(y1 = %MathContainer313); Do(z1 = %MathContainer317); Do(x2 = %MathContainer310); Do(y2 = %MathContainer314); Do(z2 = %MathContainer318); Do(x3 = %MathContainer311); Do(y3 = %MathContainer315); Do(z3 = %MathContainer319); Do(x4 = %MathContainer312); Do(y4 = %MathContainer316); Do(z4 = %MathContainer320); v1:=<x1,y1,z1>; v2:=<x2,y2,z2>; v3:=<x3,y3,z3>; v4:=<x4,y4,z4>; if nops([f])*nops([x1])*nops([y1])*nops([z1])*nops([x2])*nops([y2])*nops([z2])*nops([x3])*nops([y3])*nops([z3])*nops([x4])*nops([y4])*nops([z4])=0 then return;end if; q := simplify(int(f,[x,y,z]=Tetrahedron(v1,v2,v3,v4),inert)); Do(%MathContainer321 = q); end module; end use; JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer321); if nops([Q])=0 then return;end if; Do(%MathContainer322 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer322); if nops([q])=0 then return;end if; Do(%MathContainer322 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer321); Do(q2 = %MathContainer322); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer322 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer322 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer322 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer308 = NULL); Do(%MathContainer321 = NULL); Do(%MathContainer322 = NULL); Do(%MathContainer309 = NULL); Do(%MathContainer313 = NULL); Do(%MathContainer317 = NULL); Do(%MathContainer310 = NULL); Do(%MathContainer314 = NULL); Do(%MathContainer318 = NULL); Do(%MathContainer311 = NULL); Do(%MathContainer315 = NULL); Do(%MathContainer319 = NULL); Do(%MathContainer312 = NULL); Do(%MathContainer316 = NULL); Do(%MathContainer320 = NULL); end use; Tabela 29 Integral tripla iterada sobre um tetraedro em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiYtSSNtbkdGJDYlUSIzRidGNUY3L0YzUSV0cnVlRidGNS9GOFEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGNw== JSFH

JSFH Tabela 30 cont\303\251m um modelo de tarefa utilizada para calcular a integral da fun\303\247\303\243o 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 sobre a regi\303\243o do primeiro octante limitado pelas superf\303\255cies LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 e 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, situada no interior do cilindro, cuja se\303\247\303\243o transversal \303\251 limitada pelas curvas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GIzYmLUYsNiNRIUYnLUkmbXNxcnRHRiQ2Iy1GIzYlLUYsNiZRInhGJ0YvRjJGNUYyRjxGMkY8RlNGMkY8 e 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. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial\342\211\273Integra\303\247\303\243o \342\211\273Integra\303\247\303\243o M\303\272ltipla\342\211\2733-D\342\211\273Sobre um Cubo Integrar 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 sobre uma Regi\303\243o Geral 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRS1JI21pR0YkNiZRImZGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JS1GIzYpLUZJNiZRInhGJ0ZMRi9GTy1GLDYuUSIsRidGL0YyRjUvRjhGTkY5RjtGPUY/RkFGQy9GR1EsMC4zMzMzMzMzZW1GJy1GSTYmUSJ5RidGTEYvRk9GWS1GSTYmUSJ6RidGTEYvRk9GL0YyRi9GMi1GLDYuUSI9RidGL0YyRjVGN0Y5RjtGPUY/RkEvRkRRLDAuMjc3Nzc3OGVtRicvRkdGY29GL0Yy use DocumentTools in Do(%MathContainer323 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3243 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3244 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIyRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3245 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3246 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3247 = NULL); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiYtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGMkY1RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi5RIj1GJ0Y1RkEvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZaRjVGQQ==use DocumentTools in Do(%MathContainer3248 = NULL); end use; JSFH use DocumentTools,VectorCalculus in module() local f, q, x1,x2,y1,y2,z1,z2; Do(f = %MathContainer323); Do(z2 = %MathContainer324); Do(z1 = %MathContainer327); Do(y2 = %MathContainer325); Do(y1 = %MathContainer328); Do(x2 = %MathContainer326); Do(x1 = %MathContainer329); if nops([f])*nops([x1])*nops([x2])*nops([y1])*nops([y2])*nops([z1])*nops([z2])=0 then return;end if; q := int(f,[x,y,z]=Region(x1..x2,y1..y2,z1..z2),inert); Do(%MathContainer330 = q); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIn5GJ0YyL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk4tRiw2JlEjZHlGJ0YvRjJGNUY4LUYsNiZRI2R4RidGL0YyRjVGMkY8 JSFH JSFH use DocumentTools,VectorCalculus in module() local Q; Do(Q = %MathContainer330); if nops([Q])=0 then return;end if; Do(%MathContainer331 = value(Q)); end module; end use; JSFH JSFHuse DocumentTools in module() local q; Do(q = %MathContainer331); if nops([q])=0 then return;end if; Do(%MathContainer331 = simplify(q)); end module; end use; use DocumentTools in module() local q1,q2; Do(q1 = %MathContainer330); Do(q2 = %MathContainer331); if nops([q1])=0 and nops([q2])=0 then return; end if; if nops([q1])=0 and nops([q2])<>0 then Do(%MathContainer331 = evalf(q2));end if; if nops([q1])<>0 and nops([q2])=0 then Do(%MathContainer331 = evalf(q1));end if; if nops([q1])<>0 and nops([q2])<>0 then Do(%MathContainer331 = evalf(q1));end if; end module; end use; use DocumentTools in Do(%MathContainer323 = NULL); Do(%MathContainer324 = NULL); Do(%MathContainer327 = NULL); Do(%MathContainer325 = NULL); Do(%MathContainer328 = NULL); Do(%MathContainer326 = NULL); Do(%MathContainer329 = NULL); Do(%MathContainer330 = NULL); Do(%MathContainer331 = NULL); end use; Tabela 30 Integral tripla iterada sobre uma regi\303\243o geral em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JlEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjQvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiYtSSNtbkdGJDYlUSIzRidGNUY3L0YzUSV0cnVlRidGNS9GOFEnaXRhbGljRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjVGNw==

JSFH O Maplet de integra\303\247\303\243o m\303\272ltipla fornece acesso alternativo para o comando int como modificado nos pacotes VectorCalculus. Tabela 46 cont\303\251m o "conte\303\272do m\303\255nimo" do modelo de tarefa. O "conte\303\272do padr\303\243o" incluiria a se\303\247\303\243o Ajuda Prolongada, o que n\303\263s colocamos aqui, fora do quadro 46.

JSFH O Multiple Integration Maplet proporciona acesso simplificado ao comando int como modificado nos pacotes VectorCalculus. Estas modifica\303\247\303\265es permitem que int crie integrais (iterada) m\303\272ltiplas, tanto ativas e inertes. Um n\303\272mero de regi\303\265es pr\303\251-definidas de integra\303\247\303\243o s\303\243o conhecidos para o comando, que tamb\303\251m admite dom\303\255nios definidos pelo usu\303\241rio. JSFHO Maplet, acessado a partir do modelo de tarefas apresentados na Tabela 31, cont\303\251m tr\303\252s pain\303\251is. O painel inicial \303\251 mostrado na Figura 1. 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 1 Painel inicial para o Maplet de Integra\303\247\303\243o M\303\272ltipla Um integrando \303\251 inserido no campo designado como "Function =". Por padr\303\243o, o Maplet espera uma integral tripla, mas isso pode ser alterado clicando no bot\303\243o 2D ao lado direito de "Dimensions." As vari\303\241veis de integra\303\247\303\243o s\303\243o inseridas nos campos ao lado direito de 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 (ou 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 caso 2D). Assim, se a integra\303\247\303\243o \303\251 sobre um disco, o fundamental comando int ir\303\241 mudar para coordenadas polares, com a primeira vari\303\241vel sendo a coordenada radial. (Para esses casos, int incluir\303\241 automaticamente o Jacobiano apropriado.) Regi\303\265es de integra\303\247\303\243o s\303\243o acessadas clicando nos bot\303\265es "Edit 3D Region" ou "Edit 2D Region" . Os pain\303\251is que se abrem s\303\243o mostrados nas Figuras 2 e 3, respectivamente. JSFH 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2 Regi\303\265es de integra\303\247\303\243o para integrais triplasFigura 3 Regi\303\265es de integra\303\247\303\243o para integrais duplas Tr\303\252s regi\303\265es 3D pr\303\251-definidas s\303\243o reconhecidas, nomeadamente, a esfera, paralelep\303\255pedo, e o tetraedro. A regi\303\243o 3D geral est\303\241 inscrita fornecendo as fun\303\247\303\265es limitadas apropriadas na se\303\247\303\243o designada por "3D Region." Quatro regi\303\265es 2D pr\303\251-definidas s\303\243o reconhecidas, nomeadamente, o tri\303\242ngulo, ret\303\242ngulo, c\303\255rculo e a elipse. Claramente, por "circle" que significa o fechamento, ou mais apropriadamente, o disco. Tanto o c\303\255rculo e elipse podem ser subdivididos, escolhendo a op\303\247\303\243o Sector. A regi\303\243o 2D geral est\303\241 inscrita fornecendo as fun\303\247\303\265es limitadas apropriadas na se\303\247\303\243o designada por "2D Region." JSFH

Resumidamente, h\303\241 dois pain\303\251is que t\303\252m que ser preenchidos para o c\303\241lculo deste Maplet. No entanto, os casos das regi\303\265es de duas e tr\303\252s dimens\303\265es s\303\243o separados, por isso h\303\241 tr\303\252s pain\303\251is poss\303\255veis que podem abrir ao usar este Maplet. Ferramentas\342\211\273Tarefas\342\211\273Pesquisa: C\303\241lculo Vetorial \342\211\273Integra\303\247\303\243o\342\211\273Multiple Integration Maplet JSFH Multiple Integration MapletPara iniciar Multiple Integration Maplet, clique no bot\303\243o \303\240 direita.use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() MultipleIntInteractive := proc() local MultipleIntMaplet, workML, fluxML, numSegPages, chosenSegments, segments, started, goterror, evalNumeric, evalSymbolic, showIntegral, showOnlyIntegral, setSector, settriangle, setrectangle, setcircle, setellipse, setregion2d, setregion3d, setsphere, setparr, settetra, set2d, set3d, editRegion, editsegments, getparams, showHelp, getCheckValue; set2d := proc() use Maplets[Tools] in Set( dimtext_(caption)= " [x, y] = [" ); Set( zseperator_(caption)= "]" ); Set( end_(caption)= " " ); Set( z_(editable) = false ); Set( twodradio_ = true ); Set( edit2dregbut_(visible) = true ); Set( edit3dregbut_(visible) = false ); end use; end proc: set3d := proc() use Maplets[Tools] in Set( dimtext_(caption)= "[x, y, z] = [" ); Set( zseperator_(caption)= "," ); Set( end_(caption)= "]" ); Set( z_(editable) = true ); Set( threedradio_ = true ); Set( edit2dregbut_(visible) = false ); Set( edit3dregbut_(visible) = true ); end use; end proc: # Sets the triangle radio button to be selected settriangle := proc() use Maplets[Tools] in set2d(); Set(triangleradio_= true ); end use; end proc: # Sets the rectangle radio button to be selected setrectangle := proc() use Maplets[Tools] in set2d(); Set(rectangleradio_= true ); end use; end proc: # Sets the circle radio button to be selected setcircle := proc() use Maplets[Tools] in set2d(); Set(circleradio_= true ); end use; end proc: # Sets the ellipse radio button to be selected setellipse := proc() use Maplets[Tools] in set2d(); Set(ellipseradio_= true ); end use; end proc: # Sets the Sector radio button to be selected setSector := proc() use Maplets[Tools] in set2d(); Set(Sectorcheck_= true ); end use; end proc: # Sets the 2d Region radio button to be selected setregion2d := proc() use Maplets[Tools] in set2d(); Set(region2dradio_= true ); end use; end proc: # Sets the 3d Region radio button to be selected setregion3d := proc() use Maplets[Tools] in set3d(); Set(region3dradio_= true ); end use; end proc: # Sets the sphere radio button to be selected setsphere := proc() use Maplets[Tools] in set3d(); Set(sphereradio_= true ); end use; end proc: # Sets the parrallelepiped radio button to be selected setparr := proc() use Maplets[Tools] in set3d(); Set(parrradio_= true ); end use; end proc: # Sets the tetrahedron radio button to be selected settetra := proc() use Maplets[Tools] in set3d(); Set(tetraradio_= true ); end use; end proc: # Gets the current value from control and checks to see if # its type matches valType if not # it asks the user to enter a correct value using valName as the # name of the control # Also if the control doesn't match it sets the global variable # goterror to be true getCheckValue := proc ( control, valType, valName::string ) local value, errstring; use Maplets[Tools], Maplets[Utilities] in value := Get ( control ); value := parse( value ); if not ( type ( value, valType ) ) then errstring :=sprintf ( "Please enter an %s value for %s", valType, valName ); ErrorDialog('title' = "Missing/Incorect Value", 'errormessage' = errstring); value := 0; goterror := true; end if; end use; value; end proc: # Gets all the neccecary parameters for the line integration # and returns them getparams := proc() local Sectorable, r, point, range, h, k, a, b, par, eqn, start, finish, F, dom, domstr, command, params; use Maplets[Tools] in goterror := false; if ( Get ( triangleradio_::boolean ) = true ) then point[1][x] := getCheckValue ( trianglep1x_, algebraic, "Triangle Point 1 x" ); point[1][y] := getCheckValue ( trianglep1x_, algebraic, "Triangle Point 1 y" ); point[2][x] := getCheckValue ( trianglep2x_, algebraic, "Triangle Point 2 x" ); point[2][y] := getCheckValue ( trianglep2y_, algebraic, "Triangle Point 2 y" ); point[3][x] := getCheckValue ( trianglep3x_, algebraic, "Triangle Point 3 x" ); point[3][y] := getCheckValue ( trianglep3y_, algebraic, "Triangle Point 3 y" ); dom := Triangle ( < point[1][x], point[1][y] >, < point[2][x], point[2][y] >, < point[3][x], point[3][y] > ); domstr := sprintf ( "Triangle ( < %a, %a >, < %a, %a >, < %a, %a > )", point[1][x], point[1][y], point[2][x], point[2][y], point[3][x], point[3][y] ); elif ( Get ( rectangleradio_::boolean ) = true ) then range[x][min] := getCheckValue ( recxmin_, algebraic, "Rectangle x minimum" ); range[x][max] := getCheckValue ( recxmax_, algebraic, "Rectangle x maximum" ); range[y][min] := getCheckValue ( recymin_, algebraic, "Rectangle y minimum" ); range[y][max] := getCheckValue ( recymax_, algebraic, "Rectangle y maximum" ); dom := Rectangle ( range[x][min]..range[x][max], range[y][min]..range[y][max] ); domstr := sprintf("Rectangle ( %a..%a, %a..%a )", range[x][min], range[x][max], range[y][min],range[y][max] ); elif ( Get ( circleradio_::boolean ) = true ) then h := getCheckValue ( circlecenterx_, algebraic, "Circle center h" ); k := getCheckValue ( circlecentery_, algebraic, "Circle center k" ); r := getCheckValue ( circleradius_, algebraic, "Circle radius" ); dom := Circle ( < h , k >, r ); domstr := sprintf ("Circle ( < %a , %a >, %a )", h, k, r ); Sectorable := true; elif ( Get ( ellipseradio_::boolean ) = true ) then h := getCheckValue ( ellipsecenterx_, algebraic, "Ellipse center h" ); k := getCheckValue ( ellipsecentery_, algebraic, "Ellipse center k" ); a := getCheckValue ( ellipsesemimajor_, algebraic, "Ellipse Semimajor axis" ); b := getCheckValue ( ellipsesemiminor_, algebraic, "Ellipse Semiminor axis" ); if not ( goterror ) then eqn := -1 + (x - h)^2 / a^2 + (y - k)^2 / b^2; end if; Sectorable := true; dom := Ellipse ( eqn ); domstr := sprintf ("Ellipse ( %a )", eqn ); elif ( Get ( region2dradio_::boolean ) = true ) then range[x][min] := getCheckValue ( region2dxmin_, algebraic, "2D Region x minimum" ); range[x][max] := getCheckValue ( region2dxmax_, algebraic, "2D Region x maximum" ); range[y][min] := getCheckValue ( region2dymin_, algebraic, "2D Region y minimum" ); range[y][max] := getCheckValue ( region2dymax_, algebraic, "2D Region y maximum" ); dom := Region ( range[x][min]..range[x][max], range[y][min]..range[y][max] ); domstr := sprintf("Region ( %a..%a, %a..%a )", range[x][min], range[x][max], range[y][min],range[y][max] ); elif ( Get ( region3dradio_::boolean ) = true ) then range[x][min] := getCheckValue ( region3dxmin_, algebraic, "3D Region x minimum" ); range[x][max] := getCheckValue ( region3dxmax_, algebraic, "3D Region x maximum" ); range[y][min] := getCheckValue ( region3dymin_, algebraic, "3D Region y minimum" ); range[y][max] := getCheckValue ( region3dymax_, algebraic, "3D Region y maximum" ); range[z][min] := getCheckValue ( region3dzmin_, algebraic, "3D Region z minimum" ); range[z][max] := getCheckValue ( region3dzmax_, algebraic, "3D Region z maximum" ); dom := Region ( range[x][min]..range[x][max], range[y][min]..range[y][max], range[z][min]..range[z][max] ); domstr := sprintf("Region ( %a..%a, %a..%a, %a..%a )", range[x][min], range[x][max], range[y][min], range[y][max], range[z][min], range[z][max] ); elif ( Get ( sphereradio_::boolean ) = true ) then point[1][x] := getCheckValue ( spherecx_, algebraic, "Sphere center x" ); point[1][y] := getCheckValue ( spherecy_, algebraic, "Sphere center y" ); point[1][z] := getCheckValue ( spherecy_, algebraic, "Sphere center z" ); r := getCheckValue ( spherer_, algebraic, "Sphere radius" ); dom := Sphere ( < point[1][x], point[1][y], point[1][z] >, r ); domstr := sprintf ("Sphere ( < %a , %a, %a >, %a )", point[1][x], point[1][y], point[1][z], r ); elif ( Get ( parrradio_::boolean ) = true ) then range[x][min] := getCheckValue ( parrxmin_, algebraic, "Parallelepiped x minimum" ); range[x][max] := getCheckValue ( parrxmax_, algebraic, "Parallelepiped x maximum" ); range[y][min] := getCheckValue ( parrymin_, algebraic, "Parallelepiped y minimum" ); range[y][max] := getCheckValue ( parrymax_, algebraic, "Parallelepiped y maximum" ); range[z][min] := getCheckValue ( parrzmin_, algebraic, "Parallelepiped z minimum" ); range[z][max] := getCheckValue ( parrzmax_, algebraic, "Parallelepiped z maximum" ); dom := Parallelepiped ( range[x][min]..range[x][max], range[y][min]..range[y][max], range[z][min]..range[z][max] ); domstr := sprintf("Parallelepiped ( %a..%a, %a..%a, %a..%a )", range[x][min], range[x][max], range[y][min], range[y][max], range[z][min], range[z][max] ); elif ( Get ( tetraradio_::boolean ) = true ) then point[1][x] := getCheckValue ( tetrav1x_, algebraic, "Tetrahedron v1 x" ); point[1][y] := getCheckValue ( tetrav1y_, algebraic, "Tetrahedron v1 y" ); point[1][z] := getCheckValue ( tetrav1z_, algebraic, "Tetrahedron v1 z" ); point[2][x] := getCheckValue ( tetrav1x_, algebraic, "Tetrahedron v2 x" ); point[2][y] := getCheckValue ( tetrav1y_, algebraic, "Tetrahedron v2 y" ); point[2][z] := getCheckValue ( tetrav1z_, algebraic, "Tetrahedron v2 z" ); point[3][x] := getCheckValue ( tetrav1x_, algebraic, "Tetrahedron v3 x" ); point[3][y] := getCheckValue ( tetrav1y_, algebraic, "Tetrahedron v3 y" ); point[3][z] := getCheckValue ( tetrav1z_, algebraic, "Tetrahedron v3 z" ); point[4][x] := getCheckValue ( tetrav1x_, algebraic, "Tetrahedron v4 x" ); point[4][y] := getCheckValue ( tetrav1y_, algebraic, "Tetrahedron v4 y" ); point[4][z] := getCheckValue ( tetrav1z_, algebraic, "Tetrahedron v4 z" ); dom := Tetrahedron ( < point[1][x], point[1][y], point[1][z] >, < point[2][x], point[2][y], point[2][z] >, < point[3][x], point[3][y], point[3][z] >, < point[4][x], point[4][y], point[4][z] > ); domstr := sprintf ("Tetrahedron ( < %a , %a, %a >, < %a , %a, %a >, < %a , %a, %a >, < %a , %a, %a > )", point[1][x], point[1][y], point[1][z], point[2][x], point[2][y], point[2][z], point[3][x], point[3][y], point[3][z], point[4][x], point[4][y], point[4][z] ); else end if; if ( not ( goterror) and Get( Sectorcheck_::boolean ) and Sectorable = true ) then start := getCheckValue ( Sectorstart_, algebraic, "Sector start" ); finish := getCheckValue ( Sectorfinish_, algebraic, "Sector finish" ); dom := Sector ( dom, start, finish ); domstr := sprintf ("Sector ( %s, %a, %a )", domstr, start, finish); end if; F := getCheckValue ( function_, algebraic, "Vector Field f" ); par[1] := getCheckValue ( x_, algebraic, "x Parameter" ); par[2] := getCheckValue ( y_, algebraic, "y Parameter" ); if getCheckValue ( threedradio_, boolean, "Dimension" ) then par[3] := getCheckValue ( z_, algebraic, "z Parameter" ); params := [ par[1], par[2], par[3] ]; else params := [ par[1], par[2] ]; end if; command := sprintf ("int( %a, %a=%s )", F, params, domstr ); Set ( command_= command ); (F, params=dom ); end use; end proc: evalNumeric := proc() local result, parms; use Maplets[Tools] in parms := getparams(); if ( not ( goterror ) ) then result := VectorCalculus:-int( parms ); Set ( result_ = evalf( result ) ); showIntegral(); else Set ( result_ = "Error" ); goterror := false; end if; end use; end proc: evalSymbolic := proc() local result, parms; use Maplets[Tools] in parms := getparams(); if ( not ( goterror ) ) then result := VectorCalculus:-int( parms ); Set ( result_ = result ); showIntegral(); else Set ( result_ = "Error" ); goterror := false; end if; end use; end proc: showIntegral := proc() local intres, parms; use Maplets[Tools] in parms := getparams(); if ( not ( goterror ) ) then intres := VectorCalculus:-int( parms, inert ); Set ( integral_ = intres ); else Set ( integral_ = "Error" ); goterror := false; end if; end use; end proc: showOnlyIntegral := proc() use Maplets[Tools] in Set ( result_ = "" ); showIntegral(); end use; end proc: showHelp := proc() local MAPLET, message; message := " To use this Maplet, first enter the integrand of the iterated integral. Then choose 2D for a double integral or 3D for a triple integral. Next, in the fields to the right of '[x,y] =' (or '[x,y,z] =') enter the integration variables, which should agree with those in the integrand. Now, click on 'Enter 2D Region' or 'Enter 3D Region', depending on which type of integral you have chosen. In the window that appears, choose a region over which the integration is to take place. Enter appropriate parameters for the chosen region: - Triangle - Enter the coordinates for each of the triangle's vertices. - Rectangle - Enter the left and right bounds for x, and the lower and upper bounds for y. - Circle - Enter the coordinates of the center of the circle and the circle's radius. - Ellipse - Enter the coordinates for the center of the ellipse as well as the lengths of the semimajor and semiminor axes. - 2D Region - If the variables are [x, y] then the iterated integral formed will be dydx. Enter the bounds of the region so as to be consistent with this order of integration. - Sphere - Enter the coordinates of the center of the sphere and the sphere's radius. - Parallelepiped - Enter the bounding values for the x, y, and z coordinates, thereby defining a rectangular box in three dimensions. - Tetrahedron - Enter the coordinates for the four points of the tetrahedron. - 3D Region - If the variables are [x,y,z] then the iterated integral formed will be dz dy dx. Enter the bounds of the region so as to be consistent with this order of integration. To integrate over a sector of a circle or ellipse, select sector, and provide the initial and terminal angles defining the sector. Finally, Click on 'Display Integral' to show the integral that will be evaluated. Click on 'Symbolic Evaluation' to evaluate the integral exactly. Click on 'Numeric Evaluation' to obtain a floating-point answer. The integral and its value will be displayed in the bottom left and right windows, respectively. The Maple command to generate the result will be displayed in the bottom field"; use Maplets[Elements] in MAPLET := Maplet( MessageDialog( type=information, caption=message, title="Multiple Integration Maplet Help", onapprove=Shutdown() ) ): Maplets[Display](MAPLET); end use; end proc; MultipleIntMaplet := proc() local OPTIONS, STARTUP, WINDOW, MAPLET, COL1, COL2, COL3, LINE1, LINE2, LINE3, TWODWIN, THREEDWIN, EDITREGION, SECTOR, CIRCLE, ELLIPSE, TRIANGLE, PARALLELEPIPED, BUTTONS, RESULT, GROUPS, BUTRES, INTEGRAL, HELP, CLOSE, RECTANGLE, SPHERE, TETRAHEDRON, REGION2D, REGION3D, SETREGION, SETTRIANGLE, SETRECTANGLE, SETCIRCLE, SETELLIPSE, SETREGION2D, SETREGION3D, SETSPHERE, SETPARR, SETTETRA, SETSECTOR, SET2D, SET3D, EVALSYMBOLIC, EVALNUMERIC, SHOWINTEGRAL, FUNCTION, TWOD, THREED, OUTPUT; use Maplets, Maplets[Elements] in goterror := false; OPTIONS := title="Multiple Integration Maplet"; SETREGION := Evaluate ( function=setregion ); SETTRIANGLE := Evaluate ( function=settriangle ); SETRECTANGLE := Evaluate ( function=setrectangle ); SETCIRCLE := Evaluate ( function=setcircle ); SETELLIPSE := Evaluate ( function=setellipse ); SETREGION2D := Evaluate ( function=setregion2d ); SETREGION3D := Evaluate ( function=setregion3d ); SETSPHERE := Evaluate ( function=setsphere ); SETPARR := Evaluate ( function=setparr ); SETTETRA := Evaluate ( function=settetra ); SETSECTOR := Evaluate ( function=setSector ); EDITREGION := Action ( Evaluate ( function=editRegion ) ); SET2D := Evaluate ( function=set2d ); SET3D := Evaluate ( function=set3d ); EVALSYMBOLIC := Evaluate ( function=evalSymbolic ); EVALNUMERIC := Evaluate ( function=evalNumeric ); SHOWINTEGRAL := Evaluate ( function=showOnlyIntegral ); CLOSE := Shutdown( ); HELP := Evaluate ( function=showHelp ); TRIANGLE := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[triangleradio_]("Triangle", group=path_, onclick=SETTRIANGLE) ) ), BoxColumn ( inset = 0, BoxRow ( inset = 0, "Point 1", "x =", TextField[trianglep1x_](width=4, onchange=SETTRIANGLE), "y =", TextField[trianglep1y_](width=4, onchange=SETTRIANGLE) ), BoxRow ( inset = 0, "Point 2", "x =", TextField[trianglep2x_](width=4, onchange=SETTRIANGLE), "y =", TextField[trianglep2y_](width=4, onchange=SETTRIANGLE) ), BoxRow ( inset = 0, "Point 3", "x =", TextField[trianglep3x_](width=4, onchange=SETTRIANGLE), "y =", TextField[trianglep3y_](width=4, onchange=SETTRIANGLE) ) ) ); RECTANGLE := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[rectangleradio_] ("Rectangle", group=path_, onclick=SETRECTANGLE) ) ), BoxColumn ( inset=0, BoxRow( inset=0, "x =", TextField[recxmin_](width=4, onchange=SETRECTANGLE), "..", TextField[recxmax_](width=4, onchange=SETRECTANGLE) ), BoxRow( inset=0, "y =", TextField[recymin_](width=4, onchange=SETRECTANGLE), "..", TextField[recymax_](width=4, onchange=SETRECTANGLE) ) ) ) ; CIRCLE := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[circleradio_]("Circle", group=path_, onclick=SETCIRCLE) ) ), BoxColumn ( halign=left, BoxRow ( "( h, k ) =", "(", TextField[circlecenterx_](width=4, onchange=SETCIRCLE), ",", TextField[circlecentery_](width=4, onchange=SETCIRCLE), ")" ), BoxRow ( HorizontalGlue(), "r =", TextField[circleradius_](onchange=SETCIRCLE, width=4) ) ) ) ; ELLIPSE := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[ellipseradio_]("Ellipse", group=path_, onclick=SETELLIPSE) ) ) , BoxColumn ( inset=0, BoxRow ( halign=right, inset = 0, "( h, k ) = (", TextField[ellipsecenterx_]( width =5, onchange=SETELLIPSE), ",", TextField[ellipsecentery_]( width=5, onchange=SETELLIPSE), ")" ), BoxRow ( halign=right, inset = 0, "semimajor axis", "=", TextField[ellipsesemimajor_]( width=5, onchange=SETELLIPSE ) ), BoxRow( halign=right, inset = 0, "semiminor axis", "=", TextField[ellipsesemiminor_]( width=5, onchange=SETELLIPSE ) ) ) ); SECTOR := BoxRow ( inset=0, BoxColumn (inset=0, CIRCLE, ELLIPSE), BoxColumn ( inset=0, CheckBox[Sectorcheck_]( "Sector" ), BoxRow( inset=0, halign=right, "Start Angle", TextField[Sectorstart_]( width=4, onchange=SETSECTOR ) ), BoxRow( inset=0, halign=right, "Finish Angle", TextField[Sectorfinish_](width=4, onchange=SETSECTOR) ) ) ); REGION2D := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[region2dradio_]("2D Region", group=path_, onclick=SETREGION2D) ) ), BoxColumn ( inset=0, BoxRow( inset=0, "x =", TextField[region2dxmin_](width=4, onchange=SETREGION2D), "..", TextField[region2dxmax_](width=4, onchange=SETREGION2D) ), BoxRow( inset=0, "y =", TextField[region2dymin_](width=4, onchange=SETREGION2D), "..", TextField[region2dymax_](width=4, onchange=SETREGION2D) ) ) ) ; REGION3D := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[region3dradio_]("3D Region", group=path_, onclick=SETREGION3D) ) ), BoxColumn ( inset=0, BoxRow( inset=0, "x =", TextField[region3dxmin_](width=4, onchange=SETREGION3D), "..", TextField[region3dxmax_](width=4, onchange=SETREGION3D) ), BoxRow( inset=0, "y =", TextField[region3dymin_](width=4, onchange=SETREGION3D), "..", TextField[region3dymax_](width=4, onchange=SETREGION3D) ), BoxRow( inset=0, "z =", TextField[region3dzmin_](width=4, onchange=SETREGION3D), "..", TextField[region3dzmax_](width=4, onchange=SETREGION3D) ) ) ) ; SPHERE := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[sphereradio_]("Sphere", group=path_, onclick=SETSPHERE) ) ), BoxColumn ( BoxRow( "Center (x, y, z) = (", TextField[spherecx_](width=4, onchange=SETSPHERE), ",", TextField[spherecy_](width=4, onchange=SETSPHERE), ",", TextField[spherecz_](width=4, onchange=SETSPHERE), ")" ), BoxColumn ( BoxRow( "Radius = ", TextField[spherer_](width=4, onchange=SETSPHERE) ) ) ) ); PARALLELEPIPED := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[parrradio_]("Parallelepiped", group=path_, onclick=SETPARR) ) ), BoxColumn ( inset=0, BoxRow ( inset=0, "x =", TextField[parrxmin_](width=4, onchange=SETPARR), "..", TextField[parrxmax_](width=4, onchange=SETPARR) ), BoxRow ( inset=0, "y =", TextField[parrymin_](width=4, onchange=SETPARR), "..", TextField[parrymax_](width=4, onchange=SETPARR) ), BoxRow ( inset=0, "z =", TextField[parrzmin_](width=4, onchange=SETPARR), "..", TextField[parrzmax_](width=4, onchange=SETPARR) ) ) ) ; TETRAHEDRON := BoxRow( inset=0, border =true, BoxColumn ( inset=0, halign=left, BoxRow ( inset=0, RadioButton[tetraradio_]("Tetrahedron", group=path_, onclick=SETTETRA) ) ), BoxColumn ( inset = 0, BoxRow ( inset = 0, "p1 = (", TextField[tetrav1x_](width=4, onchange=SETTETRA), ",", TextField[tetrav1y_](width=4, onchange=SETTETRA), ",", TextField[tetrav1z_](width=4, onchange=SETTETRA), ")" ), BoxRow ( inset = 0, "p2 = (", TextField[tetrav2x_](width=4, onchange=SETTETRA), ",", TextField[tetrav2y_](width=4, onchange=SETTETRA), ",", TextField[tetrav2z_](width=4, onchange=SETTETRA), ")" ), BoxRow ( inset = 0, "p3 = (", TextField[tetrav3x_](width=4, onchange=SETTETRA), ",", TextField[tetrav3y_](width=4, onchange=SETTETRA), ",", TextField[tetrav3z_](width=4, onchange=SETTETRA), ")" ), BoxRow ( inset = 0, "p4 = (", TextField[tetrav4x_](width=4, onchange=SETTETRA), ",", TextField[tetrav4y_](width=4, onchange=SETTETRA), ",", TextField[tetrav4z_](width=4, onchange=SETTETRA), ")" ) ) ) ; RESULT := MathMLViewer[result_] (height=70, width=150); INTEGRAL := MathMLViewer[integral_] (height=70, width=500); FUNCTION := BoxColumn ( BoxRow ( "Function = ",TextField[function_]( width = 60) ), BoxRow ( "Dimensions:", RadioButton[twodradio_] ("2D", group=dimension_, onclick=SET2D), RadioButton[threedradio_] ("3D", value=true, group=dimension_, onclick=SET3D), Button[edit2dregbut_]("Edit 2D Region", visible = false, width = 150, onclick= RunWindow( twodwin_) ), Button[edit3dregbut_]("Edit 3D Region", visible = true, width = 150, onclick= RunWindow( threedwin_) ), Label[dimtext_] ("[x, y, z] = ["), TextField[x_](width=4), ",", TextField[y_](width=4), Label[zseperator_](","), TextField[z_](width=4), Label[end_]("]") ) ); TWOD := BoxColumn[twodcol_] ( TRIANGLE, RECTANGLE, SECTOR, REGION2D, Button( "OK", CloseWindow( twodwin_ ) ) ); THREED := BoxColumn[threedcol_] ( SPHERE, PARALLELEPIPED, TETRAHEDRON, REGION3D, Button( "OK", CloseWindow( threedwin_ ) ) ); TWODWIN := Window[twodwin_]( title="Enter 2D Region", TWOD ); THREEDWIN:= Window[threedwin_]( title="Enter 3D Region", THREED ); BUTTONS[1] := BoxRow ( Button( "Display Integral", SHOWINTEGRAL, width=170 ), Button( "Symbolic Evaluation", EVALSYMBOLIC, width=170 ), Button( "Numeric Evaluation", EVALNUMERIC, width=170 ) ); BUTTONS[2] := BoxRow ( Button ( "Help", HELP, width=80 ), Button ( "Close", CLOSE, width=80 ) ); OUTPUT := BoxColumn ( BoxRow ( INTEGRAL, "=", RESULT ), BoxRow( "Maple Command:", TextField[command_](width=72) ) ); LINE1 := FUNCTION; LINE2 := BoxRow ( BoxColumn ( BUTTONS[1], OUTPUT, BUTTONS[2] ) ); WINDOW := Window[W_]( OPTIONS, BoxLayout ( inset=0, BoxColumn( LINE1, LINE2 ) ) ); GROUPS := ButtonGroup[type_]( ), ButtonGroup[path_](), ButtonGroup[dimension_](); MAPLET := Maplet( onstartup=RunWindow(W_), WINDOW, TWODWIN, THREEDWIN, GROUPS ); Display( MAPLET ); end use; end proc: MultipleIntMaplet(); end proc: MultipleIntInteractive(); end module; end use; Um arquivo de Ajuda abreviada est\303\241 dispon\303\255vel dentro do Maplet.Ajuda Prolongada est\303\241 dispon\303\255vel na se\303\247\303\243o attached collapsed.Inserindo Minimal Content exclui a se\303\247\303\243o de Ajuda Prolongada.Inserindo Default Content inclui a se\303\247\303\243o de Ajuda Prolongada. JSFH Tabela 31 O Multiple Integration Maplet acessado por modelo de tarefas JSFH Por exemplo, para integrar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1LUkjbW9HRiQ2LlEiLEYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEieUYnRi9GMkY1RjJGREYyRkQtRkE2LlEiPUYnRjJGREZGL0ZJRjRGSkZMRk5GUEZSL0ZVUSwwLjI3Nzc3NzhlbUYnL0ZYRlxvRj0tRkE2LlEifkYnRjJGREZGRmpuRkpGTEZORlBGUkZUL0ZYRlZGWkYyRkQ= sobre a regi\303\243o planar limitada pelas curvas 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 e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GIzYmLUYsNiNRIUYnLUkmbXNxcnRHRiQ2Iy1GIzYlLUYsNiZRInhGJ0YvRjJGNUYyRjxGMkY8RlNGMkY8, preencher o painel secund\303\241rio, conforme mostrado na Tabela 32. JSFH 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]tImoPQyM<UWDSFhV`uqYqtV<OI\\xxuYdXOKiqqYxFaM`IsKQOJPoR]q<dSgLSYIm[IWiaKIdxbdOePJOHxJ]YjLmBhqxIUT`l>DoDLY:LoianApUhiWeIWyUyUUxjalJDsqPuuQNwxOWAQreTvinf=QjiTQIuRqu]Xv`yyJYJ:hJ?XPe@vFMoxyxTeqoPqeAuB`YpIlutwddk@MYHimRiLblmPeTxTpd@yMLQriVfEuPhpWLsBIxWHrduL[plahNNERdPnXPXoMueeX;iuwyTpusX`UOURkYO_Xb_HavybvorFygx`htid;Oo\\pqt?Zdvoh__W?t=>ZLg\\oyldPtGirEF^OFfH@hIQ_JPojqq<oaiVcuGxHxvTHpVGnQNxTosRwZmGu^P_f_og_nd^ga_nRiaEqgwvikylOW_PP[c^dmIqvokqXdG@eGykwQiSAeMvmyHbCYdf>ngP[IQxsiyUWbGwwYVyhwbrgv]gcEiubgaNv;yDakgx]xoAWAUWmwca[g:_T?whe=U]UvuwGhwIn;Hl=fyaeuwsReY`Uv=wwwODkIx:gTJOgjqXGSWRMVnsCYAuKkuqaYUOocXxgAunIyQ`s]MO[XWOHMbPWkxPZQyyTlNLKBeTr=msAXM`MI<v=Qv;iLe@J:Mo<<JcPK:\\nd<J:`T?<JLeL:<SO=ZLg<BvOfveWOEV\\QyWSGPwuQcyEMWqwuvMbVmwPkhT;BFAdw_fVmsFASOaYpSGxutvEu<oHoyVOGcoQEhEy]asGuteoUHmGeEiZaUtChdKgn?V`kdfeTOQc_?UjSDEmW@;GWGg@mucOcXOgjQxyyWsUSxsg?eTKUi`?S[?gxUHOexYwf`syXOefcsWQgn[TW?GTiBmiel=GdOghOSgsUWetKOS`eSKAUlIYwOTIaiOOgP_BKOiZKwdgRYkRK]cvcDDGYqse@cRVMTlwTcui=;b_ky?QtV=WB_cQobq;J:<j^PNaLNQENjDB::::5:\"\{\}-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%]XF*-%.BOUNDS_HEIGHTG6#$"%?`F*-%)CHILDRENG6"Tabela 32 Painel secund\303\241rio para Multiple Integration Maplet JSFH O painel inicial para o Maplet \303\251 mostrado na Tabela 33. A fun\303\247\303\243o 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 \303\251 inserida, as vari\303\241veis LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn s\303\243o introduzidas, o bot\303\243o 2D \303\251 selecionado, e o painel mostrado na Tabela 32 aparece. O bot\303\243o 2D Region \303\251 selecionado naquele painel, e os limites que descrevem a regi\303\243o planar est\303\243o inseridos. JSFH 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 33 Painel inicial para o Maplet de M\303\272ltipla Integra\303\247\303\243o JSFH Ap\303\263s o painel secund\303\241rio ser fechado, os bot\303\265es Display Integral e Symbolic Evaluation s\303\243o pressionados. Observe a exibi\303\247\303\243o expl\303\255cita do relevante comando int no bot\303\243o do painel principal. H\303\241 uma falha do Multiple Integration Maplet que os modelos de tarefa nos Quadros 23, 24 e 28 de superam. Suponha, por exemplo, o integrante de 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 sobre a esfera unit\303\241ria centrada na origem deve ser calculada. O Multiple Integration Maplet iria construir a integral 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 e mostra o comando int(z, [x, y, z] = Sphere(<0, 0, 0>, 1), inert) As letras na lista 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 s\303\243o interpretadas pelo Maple como LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEnJiM5NjY7RidGL0YyRjRGNy1GLDYmUScmIzk1MjtGJ0YvRjJGNEYyRjQ=, respectivamente. O elemento de volume 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 foi correctamente inclu\303\255do, e a vari\303\241vel LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn foi correctamente convertida em coordenadas esf\303\251ricas: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUScmIzk2MTtGJy9GMEY0RjJGPC1GOTYuUSJ+RidGMkY8Rj5GQEZCRkRGRkZIRkovRk1RJjAuMGVtRicvRlBGWS1GLDYmUSRjb3NGJ0ZURjJGPC1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRJyYjOTY2O0YnRlRGMkY8RjJGPEYyRjxGMkY8. Dado que as vari\303\241veis de integra\303\247\303\243o s\303\243o realmente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JlEnJiM5NjY7RidGL0YyRjRGNy1GLDYmUScmIzk1MjtGJ0YvRjJGNEYyRjQ=, a integral desejada foi constru\303\255da adequadamente. Mostra a integral 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 requer a sintaxe 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 mas, infelizmente, o Multiple Integration Maplet n\303\243o tem provis\303\243o para a op\303\247\303\243o de incluir uma lista de nomes de vari\303\241veis dentro da defini\303\247\303\243o da regi\303\243o de integra\303\247\303\243o.

JSFH O tutor do Curvas Espaciais \303\251 uma interface para o formalismo de Frenet-Serret para curvas planas e espaciais. Assim, dada essa curva, o tutor desenha a curva e gr\303\241ficos da tr\303\255ade de vetores tangentes, normal principal, e binormal. Esses quadros podem ser animados para mover ao longo da curva. Qualquer um destes tr\303\252s vetores podem ser isolados e representados graficamente ao longo da curva. Para as curvas espaciais, o c\303\255rculo osculador e a tor\303\247\303\243o s\303\243o representados graficamente, e para qualquer curva, a curvatura \303\251 representada graficamente. Tabela 34 mostra a curva espacial padr\303\243o para este tutor. 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34 Tutor do Curvas Espaciais e sua curva espacial padr\303\243o JSFH N\303\263s modificamos as configura\303\247\303\265es ligeiramente. Em vez do 5 quadros padr\303\243o, optamos apenas 1, e usamos o bot\303\243o Plot Options para mudar o estilo de eixo para "frame" em vez do padr\303\243o "normal". O vetor tangente unit\303\241rio \303\251 desenhado em azul, a unidade (principal) normal, na cor verde; e a unidade binormal, em magenta. \303\211 claro que o formalismo Frenet-Serret tamb\303\251m est\303\241 dispon\303\255vel no Menu de Contexto, que cont\303\251m as op\303\247\303\265es TNB Frame, Tangent Vector, Principal Normal, Binormal Vector, Curvature, Torsion, e Radius of Curvature. JSFH Tamb\303\251m \303\251 poss\303\255vel executar esses c\303\241lculos gradativamente, dos primeiros princ\303\255pios, como resumimos na Tabela 35. Inicializar Carregando VectorCalculus with(VectorCalculus): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEsQmFzaXNGb3JtYXRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSZmYWxzZUYnRi9GMi8lK2V4ZWN1dGFibGVHRjwvRjNRJ25vcm1hbEYnRj8tSSNtb0dGJDYtUSI6RidGPy8lJmZlbmNlR0Y8LyUqc2VwYXJhdG9yR0Y8LyUpc3RyZXRjaHlHRjwvJSpzeW1tZXRyaWNHRjwvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGPC8lJ2FjY2VudEdGPC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlVGPUY/ 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 Definir curva 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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiZRI2RzRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2Ji1GLzYmUSNkdEYnRjJGNUY4RjJGNUY4LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZFLyUpYmV2ZWxsZWRHRjdGNS9GOVEnbm9ybWFsRic= 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

KiQpIiIjIyIiIkYkRiY=

Vetor tangente unit\303\241rio 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

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCI1cV9md3g3WW5XPQ==

Curvatura 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

IyIiIiIiIw==

Normal Principal 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

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCI1OSUpZnd4N1luVz0=

Binormal 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

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCI1bSQqZnd4N1luVz0=

Tor\303\247\303\243o 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

IyIiIiIiIw==

Tabela 35 Formalismo de Frenet-Serret gradativamente, por primeiros princ\303\255pios JSFH

JSFH TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ2MTI3Nzc2NTk1MjcwWColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJComIiIjIyIiIkYrLUkkc2luRzYkJSpwcm90ZWN0ZWRHJShfc3lzbGliRzYjJSJ0R0YtIyEiIkYrLCQqJkYrRiwtSSRjb3NHNiRGMUYyRjNGLUYsLCQqJEYrRixGLEYlTTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ2MTI3Nzc2NTk4NDE0WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJC1JJGNvc0c2JCUqcHJvdGVjdGVkRyUoX3N5c2xpYkc2IyUidEchIiIsJC1JJHNpbkc2JEYtRi5GL0YxIiIhRiU=TTdSMApJQVJUQUJMRV9TQVZFLzE4NDQ2NzQ2MTI3Nzc2NTk5MzY2WColKWFueXRoaW5nRzYiLyUnY29vcmRzRyUqY2FydGVzaWFuR1tnbCEjJSEhISIkIiQsJComIiIjIyIiIkYrLUkkc2luRzYkJSpwcm90ZWN0ZWRHJShfc3lzbGliRzYjJSJ0R0YtRiwsJComRitGLC1JJGNvc0c2JEYxRjJGM0YtIyEiIkYrLCQqJEYrRixGLEYl