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Guia de Estudo de C\303\241lculo \302\251 Maplesoft, a division of Waterloo Maple Inc., 2005 Cap\303\255tulo 21: Antiderivadas e Integrais Indefinidas

Toda a nossa aten\303\247\303\243o at\303\251 hoje tem sido sobre computa\303\247\303\243o de derivadas (derivatives). Esta unidade vira tudo de cabe\303\247a para baixo. Agora, Em vez de encontrar a derivada de uma fun\303\247\303\243o, ser\303\241 pedido para identificar uma fun\303\247\303\243o (function) baseado na informa\303\247\303\243o sobre sua derivada. Da perspectiva de deriva\303\247\303\243o (differentiation) estas fun\303\247\303\265es s\303\243o conhecidas como antiderivadas (antiderivatives). Da perspectiva de \303\241rea (area) (a ser introduzida mais tarde nos cap\303\255tulos Soma de Riemann (Riemann Sum) e Integral Definida (Definite Integral) desta unidade) faz mais sentido falar sobre integral indefinida (indefinite integral) de uma fun\303\247\303\243o. Oa objetivos deste cap\303\255tulo s\303\243o: tornar confort\303\241vel o uso da linguagem de ambos: antiderivadas e integrais definidas, demonstrar que a f\303\263rmula da derivada pode transformada em f\303\263rmula de antiderivada (ou integral indefinida), e enterder que se pode verificar (pela deriva\303\247\303\243o) se uma integral indefinida qualquer est\303\241 correta. A compreens\303\243o gr\303\241fica da antiderivada pode ser grandemente aumentada com o uso do maplet Antiderivada (Antiderivative maplet).

Os seguintes termos, neste cap\303\255tulo, t\303\252m conex\303\243o com o Dicion\303\241rio de Matem\303\241tica Maple (Maple Math Dictionary). area constant cosine curve definiteintegral denominator derivative differentiation evaluate family function graph indefiniteintegral independent variable infinite integral integrand integration interval multiple negative numerator powerrule exponent riemannsum root sign solution tables value variable zero

restart; with( plots ):

Warning, the name changecoords has been redefined

Nesta abordagem ao c\303\241lculo, a integral indefinida \303\251 definida como sendo a mesma coisa que uma antiderivada. Alguns textos desenvolvem a no\303\247\303\243o de uma antiderivada primeiro, e ent\303\243o mostra que integra\303\247\303\243o, o problema de encontrar a \303\241rea sob uma curva, requer encontrar uma antiderivada, assim neste campo a antiderivada \303\251 ent\303\243o identificada com a integral. Aqui, sobre o vazio \303\251 feita imediatamente uma ponte, e a integral indefinida \303\251 imediatamente tomada como sin\303\264nimo de antiderivada. Fa\303\247amos precisas, esta no\303\247\303\265es, pela seguinte difini\303\247\303\243o. Defini\303\247\303\243o 21.1: Antiderivada Uma fun\303\247\303\243o F \303\251 uma antiderivada, ou uma integral indefinida, de f em um intervalo (interval) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se 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 para todo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=

A defini\303\247\303\243o prov\303\252 um exame direto para determinar se F \303\251, de fato, uma antiderivada de f: derive F (em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=) e compare este resultado com f no intervalo (interval) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= Uma nota\303\247\303\243o alternativa comum para antiderivada \303\251 a nota\303\247\303\243o de integral (integral) JSFHJSFH 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 Leia a express\303\243o 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 como "a integral indefinida de 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 em rela\303\247\303\243o a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=." O primeiro s\303\255mbolo (um S alongado) \303\251 chamado de sinal de integral, o integrando (integrand) \303\251 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, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 a vari\303\241vel (variable) de integra\303\247\303\243o (integration). O sinal de integral e o dx devem ser visto como um par combinado (matched pair) -- como os par\303\252nteses esquerdo e direito. A defini\303\247\303\243o e estas notas est\303\243o cuidadosamente escritas para estabelecer que F \303\251 uma antiderivada de f (e n\303\243o que F \303\251 a antiderivada de f). A raz\303\243o para isto se tornar\303\241 clara nos exemplos.

Para explorar este enunciado 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 escreva o integrando LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== como f1 := 3*x^2 - 2: f(x) = f1;

Ly1JImZHNiI2I0kieEdGJSwmKiYiIiQiIiIpRiciIiNGK0YrRi0hIiI=

e considere as fun\303\247\303\265es F1 := x^3 - 2*x: F2 := x^3 - 3*x + 2: F3:= x^3 - 2*x + 3: F[1](x) = F1; F[2](x) = F2; F[3](x) = F3;

Ly0mSSJGRzYiNiMiIiI2I0kieEdGJiwmKiQpRioiIiRGKEYoKiYiIiNGKEYqRighIiI=

Ly0mSSJGRzYiNiMiIiM2I0kieEdGJiwoKiQpRioiIiQiIiJGLyomRi5GL0YqRi8hIiJGKEYv

Ly0mSSJGRzYiNiMiIiQ2I0kieEdGJiwoKiQpRipGKCIiIkYuKiYiIiNGLkYqRi4hIiJGKEYu

Das derivadas destas fun\303\247\303\265es, a saber, de dF1 := Diff( F1, x ): dF2 := Diff( F2, x ): dF3 := Diff( F3, x ): dF1 = value( dF1 ); dF2 = value( dF2 ); dF3 = value( dF3 );

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjLy1JJURpZmZHNiQlKnByb3RlY3RlZEdGJTYkLCYqJClJInhHRiYiIiQiIiJGNSomIiIjRjVGM0Y1ISIiRjMsJiomRjRGNSlGM0Y3RjVGNUY3RjhGKQ==

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjLy1JJURpZmZHNiQlKnByb3RlY3RlZEdGJTYkLCgqJClJInhHRiYiIiQiIiJGNSomRjRGNUYzRjUhIiIiIiNGNUYzLCYqJkY0RjUpRjNGOEY1RjVGNEY3Rik=

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjLy1JJURpZmZHNiQlKnByb3RlY3RlZEdGJTYkLCgqJClJInhHRiYiIiQiIiJGNSomIiIjRjVGM0Y1ISIiRjRGNUYzLCYqJkY0RjUpRjNGN0Y1RjVGN0Y4Rik=

se v\303\252 que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZB e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiM0YnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZB s\303\243o antiderivadas (integrais indefinidas) de f e que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZB n\303\243o \303\251 uma antiderivada de f.

Para entender porque pode existir mais que uma antiderivada de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GIzYnRistRiM2Jy1JI21uR0YkNiRRIjNGJ0ZALUY9Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYjNiZGKy1JJW1zdXBHRiQ2JUZcby1GX3A2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQEYrRkAtRj02LVEoJm1pbnVzO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJy9GVUZkcUZqcEZARitGQEYrRkA=, considere a Figura 21.1 onde os gr\303\241fico de 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, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiM0YnL0Y5USdub3JtYWxGJ0ZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGK0ZB no intervalo (interval) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21vR0YkNi1RIltGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGSi1GIzYnRistRiM2JS1GMjYtUSomdW1pbnVzMDtGJ0Y1L0Y5Rj1GOy9GP0Y9RkBGQkZERkYvRklRJjAuMGVtRicvRkxGVy1JI21uR0YkNiRRIjJGJ0Y1RjUtRjI2LVEiLEYnRjVGVC9GPEY6RlVGQEZCRkRGRkZWL0ZMUSwwLjMzMzMzMzNlbUYnRllGNS1GMjYtUSJdRidGNUY4RjtGPkZARkJGREZGRkgvRkxRLDAuMTExMTExMWVtRidGNUYrRjU= s\303\243o vistos. plot([F1, F2, F3], x=-2..2, color=[red,blue,green], legend=["y = F1", "y = F2", "y = F3" ]);

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Figura 21.1 Exemplo 21.1: O que significa para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GIzYnRistRiM2Jy1JI21uR0YkNiRRIjNGJ0ZALUY9Ni1RMSZJbnZpc2libGVUaW1lcztGJ0ZARkJGRUZHRklGS0ZNRk9GUUZULUYjNiZGKy1JJW1zdXBHRiQ2JUZcby1GX3A2JFEiMkYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQEYrRkAtRj02LVEoJm1pbnVzO0YnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yMjIyMjIyZW1GJy9GVUZkcUZqcEZARitGQEYrRkA= ter mais de uma antiderivada Observe que o gr\303\241fico de 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 \303\251 o gr\303\241fico de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUklbXN1YkdGJDYlLUYsNiVRIkZGJ0Y0RjctRiM2JC1JI21uR0YkNiRRIjFGJ0Y+Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRj5GK0Y+ deslocado verticalmente por 3, i.e., 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 O gr\303\241fico de 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 n\303\243o \303\251 um deslocamento vertical dos outros gr\303\241ficos. Em geral, qualquer deslocamento vertical de uma antiderivada \303\251 ainda uma antiderivada. Isto deve ser porque a derivada de uma constante (constant) \303\251 zero. No caso das fun\303\247\303\265es espec\303\255ficas neste exemplo, qualquer fun\303\247\303\243o da forma 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, onde LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 uma constante, \303\251 uma antiderivada de 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. Na nota\303\247\303\243o para integral indefinida, 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

A rela\303\247\303\243o entre 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 e qualquer antiderivada 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 pode ser explorada graficamente com o Maplet Antiderivada (Antiderivative maplet), eq\303\274ivalente ao inserido no Tutor Antiderivada (Antiderivative Tutor) dispon\303\255vel do Ferramentas/ Tutores C\303\241lculo (Tools/Tutors/Calculus) - menu Uma Vari\303\241vel (Single Variable). Aplicada a esta fun\303\247\303\243o, temos a Figura 21.2. 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Figura 21.2 Tutor Antiderivada (Antiderivative Tutor) aplicado a 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 A curva azul na Figura 21.2 \303\251 a antiderivada de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== que se anula em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJhRidGL0YyRjUtSSNtbkdGJDYkUSsmdW1pbnVzMDsyRidGOUY5. Se a check box Mostre o tipo de antiderivada (Show class of antiderivatives) e o bot\303\243o Display s\303\243o clicados, Figura 21.3 resulta. Cada curva verde \303\251 congruente a, e uma transla\303\247\303\243o vertical da, antiderivada azul. The blue curve in Figure 21.2 is the antiderivative of 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 that vanishes at 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. If the check box Show class of antiderivatives and the Display button are clicked, Figure 21.3 results. Each green curve is congruent to, and a vertical translation of, the blue antiderivative. 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Figura 21.3 As 20 curvas verdes s\303\243o todas antiderivadas de 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 Cada uma \303\251 a antiderivada azul, verticalmente transladada.

Cada Regra de Deriva\303\247\303\243o listada na Tabela 11.1, no Cap\303\255tulor 11, tem uma Regra de Antideriva\303\247\303\243o correspondente. Ambos os conjuntos de regras s\303\243o dados na Tabela 21.1. Nome(Name) Regra de Deriva\303\247\303\243o (Derivative Rule) Regra de Antideriva\303\247\303\243o (Antiderivative Rule) Restri\303\247\303\265es (Restrictions) Constante(Constant) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRidGKy9GOVEnbm9ybWFsRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlNGNS1JI21uR0YkNiRRIjBGJ0Y5Rjk= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JI21uR0YkNiRRIjBGJ0YvRi8= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEiQ0YnRi9GMkY5 Identidade(Identity) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JI21uR0YkNiRRIjFGJ0YvRi8= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEieEYnRi9GMi1GNjYtUScmcGx1cztGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUSJDRidGL0YyRjk= Pot\303\252ncia (Power) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dGOS9GMFEnaXRhbGljRictRks2JVEickYnRk5GUC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRks2I1EhRidGLw== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSUmbmU7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlMtSSNtbkdGJDYkUSsmdW1pbnVzMDsxRidGOUY5 Pot\303\252ncia Generalizada(Generalized Power) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRidGKy9GOVEnbm9ybWFsRic= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSUmbmU7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORlMtSSNtbkdGJDYkUSsmdW1pbnVzMDsxRidGOUY5 M\303\272ltiple de Constante (Constant Multiple) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRidGKy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRImtGJ0Y1RjgtSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RicvRjlRJ25vcm1hbEYnLyUmZmVuY2VHRkgvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGYW8tRiM2Ji1GLDYlUSJmRidGNUY4LUZSNi1RMCZBcHBseUZ1bmN0aW9uO0YnRlVGV0ZZRmVuRmduRmluRltvRl1vRl9vRmJvLUZKNiQtRiM2JC1GLDYlUSJ4RidGNUY4RlVGVUZVRitGVUZVLUZSNi1RIj1GJ0ZVRldGWUZlbkZnbkZpbkZbb0Zdby9GYG9RLDAuMjc3Nzc3OGVtRicvRmNvRmdwRk5GUUZmby1GUjYtUSgmcHJpbWU7RidGVUZXRllGZW5GZ25GaW5GW29GXW8vRmBvUSwwLjExMTExMTFlbUYnRmJvRlxwRitGVQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dGOS9GMFEnaXRhbGljRidGLw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+RitGPg== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Soma/Diferen\303\247a (Sum/Difference) 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 Seno (Sine) 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 Cosseno (Cosine) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYsNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiw2JVEjZHhGJ0Y1RjgvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRkMvJSliZXZlbGxlZEdRJmZhbHNlRidGKy1GIzYmLUYsNiVRJHNpbkYnL0Y2RkgvRjlRJ25vcm1hbEYnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RidGTy8lJmZlbmNlR0ZILyUqc2VwYXJhdG9yR0ZILyUpc3RyZXRjaHlHRkgvJSpzeW1tZXRyaWNHRkgvJShsYXJnZW9wR0ZILyUubW92YWJsZWxpbWl0c0dGSC8lJ2FjY2VudEdGSC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRl9vLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEieEYnRjVGOEZPRk9GTy1GUjYtUSI9RidGT0ZVRldGWUZlbkZnbkZpbkZbby9GXm9RLDAuMjc3Nzc3OGVtRicvRmFvRl5wLUYjNiYtRiw2JVEkY29zRidGTkZPRlFGYm9GT0YrRk8= 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 Tabela 21.1 Regras de Deriva\303\247\303\243o da Tabela 11.1 e as Regras de Antideriva\303\247\303\243o correspondentes A restri\303\247\303\243o que 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 para Regras de Pot\303\252ncia e Pot\303\252ncia Generalizada \303\251 necess\303\241ria porque n\303\243o sabemos (ainda) nenhuma fun\303\247\303\243o cuja derivada \303\251 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. O mais prov\303\241vel candidato( most likely) \303\251 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, mas sabemos que 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. Se uma vez se esquecer desta restri\303\247\303\243o e tentar aplicar a Regra de Pot\303\252ncia ou Pot\303\252ncia Generalizada (Power Rule) com 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, divis\303\243o por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNiYtRiw2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIitGJy9GOlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGUy1JI21uR0YkNiRRIjFGJ0ZARkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZobi1GVzYkUSIwRidGQEZARitGQA== ir\303\241 lembr\303\241-lo de que isto n\303\243o \303\251 poss\303\255vel. As regras de antideriva\303\247\303\243o obtidas das regras do quociente, produto, e da cadeia n\303\243o s\303\243o de interesse neste momento. Os exemplos restantes neste cap\303\255tulo demonstram a aplica\303\247\303\243o das regras listadas na Tabela 21.1.

Para a integral indefinida considerada no Exemplo 21.1, determine a fam\303\255lia (family) de todas as antiderivadas usando as Regras de Antideriva\303\247\303\243o. Apesar da Figura 21.3 mostrar 20 membros da fam\303\255lia, aqui, examinaremos os c\303\241lculos pelos quais toda a familia pode ser determinada. Os c\303\241lculos est\303\243o resumidos na Tabela 21.2. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JKG1mZW5jZWRHRiQ2JC1GIzYoLUkjbW5HRiQ2JFEiM0YnRi8tRiw2LVExJkludmlzaWJsZVRpbWVzO0YnRi9GMkY1L0Y4RjRGOi9GPUY0Rj5GQEZCRkUtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHRjkvRjBRJ2l0YWxpY0YnLUZNNiRRIjJGJ0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLDYtUSgmbWludXM7RidGL0YyRjVGU0Y6RlRGPkZAL0ZDUSwwLjI3Nzc3NzhlbUYnL0ZGRmRvRmpuRi9GLy1GWTYlUSNkeEYnRmZuRmhuRi8= JSFH Problema Original (Original Problem) JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUYsNi1RJiZpbnQ7RidGL0YyRjUvRjhRJXRydWVGJ0Y5L0Y8RkpGPUY/L0ZCUSYwLjBlbUYnL0ZFRk0tSSNtbkdGJDYkUSIzRidGLy1GLDYtUTEmSW52aXNpYmxlVGltZXM7RidGL0YyRjVGN0Y5RjtGPUY/RkxGTi1JJW1zdXBHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dGSi9GMFEnaXRhbGljRictRlA2JFEiMkYnRi8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZaNiVRI2R4RidGZ25GaW4tRiw2LVEoJm1pbnVzO0YnRi9GMkY1RjdGOUY7Rj1GP0ZBRkRGRkZbb0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Regra da Diferen\303\247a (Difference Rule) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Regra de M\303\272ltiplo de Constante(duas vezes)(Constant Multiple Rule(twice)) 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 Regras de Pot\303\252ncia e Identidade (Power and Identity Rules) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYyLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1JI21uR0YkNiRRIjNGJ0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjIyMjIyMjJlbUYnL0ZFRmduLUZTNiRRIjJGJ0YvLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVGYG9GSS1GLDYtUScmcGx1cztGJ0YvRjJGNUY3RjlGO0Y9Rj9GZm5GaG5GUkZcby1JJW1zdWJHRiQ2JS1GSjYlUSJDRidGTUZQLUZTNiRRIjFGJ0YvLyUvc3Vic2NyaXB0c2hpZnRHRlgtRiw2LUZlbkYvRjJGNUY3RjlGO0Y9Rj9GQUZERmluRlxvLUZmbzYlRmhvRmluRl5wLUZKNiNRIUYnRi8= simplifica\303\247\303\243o alg\303\251brica (algebraic simplification) 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 reescrever a constante como C (rewrite constant as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIilGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRidGOQ== Tabela 21.2 Anota\303\247\303\265es de c\303\241lculos para o Exemplo 21.1 Note que as constantes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjFGJy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRj8= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21uR0YkNiRRIjJGJy9GOVEnbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0YrRj8= poderiam ser omitidas quando as Regras de Pot\303\252ncia e Identidade foram aplicadas, desde que a constante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= seja incluida no final.

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique. with(RandomTools): randomize(): nn := Generate(integer(range=1..4)); fn := sort(Generate(polynom(integer(range=-20..20),x,degree=nn)),x); Fn := Int(fn,x);

IiIi

LCZJInhHNiIiIzciIz8iIiI=

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJkkieEdGJyIjNyIjPyIiIkYq

JSFH

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question. Avalie `$Fn` (sugest\303\243o#1: N\303\243o esque\303\247a a constante no final) JSFH

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed. value(Fn)+C; JSFH

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region. evalb(`$ANSWER`-`$RESPONSE`=0);

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints. Don't forget the constant at the end. Replace this text with hint 2. Replace this text with hint 3. with(StringTools): with(DocumentTools): response := GetProperty(`TextArea0`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't&MediumSpace;forget&MediumSpace;the&MediumSpace;constant&MediumSpace;at&MediumSpace;the&MediumSpace;end.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response. Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea0`, `value`); ANSWER := value(Fn)+C; if evalb(ANSWER-eval(parse(StudentResponse))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="&lt;NO RESPONSE&gt;"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect.&nbsp;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer:&nbsp;</mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>20</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mn>6</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>20</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

A Tabela 21.3 resume os c\303\241lculos pelos quais a fam\303\255lia completa de antiderivadas determinadas por 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn \303\251 obtida. As Regras de Antideriva\303\247\303\243o apropriadas s\303\243o identificadas \303\240 direita da Tabela 21.3. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn JSFH Probema Original (Original Problem) 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Regras da Soma e M\303\272ltiplo de Constante (Sum and Constant Multiple Rules) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMkYnRi9GLw== 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 Regras de Pot\303\252ncia e do Cosseno (Power and Cosine Rules) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JFEiM0YnRkFGQS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRj42LVEnJnBsdXM7RidGQUZDRkZGSEZKRkxGTkZQRlJGVS1JJm1mcmFjR0YkNigtRlg2JFEiMkYnRkFGVy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZm8vJSliZXZlbGxlZEdGRUYrRkE= 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 Simplifica\303\247\303\243o Alg\303\251brica (Algebraic Simplification) Tabela 21.3 Exemplo 21.3: Aplica\303\247\303\243o das Regras de Antideriva\303\247\303\243o para 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 Para confirmar este resultado simplesmente compute a derivada desta resposta, entrando com ans3 := -2/(3*x^3) + 2/3*x^(3/2) - 3*cos(x) + C;

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkklYW5zM0dGJiwqKiYjIiIjIiIkIiIiKUkieEdGJkYwISIiRjQqJkYuRjEpRjMjRjBGL0YxRjEqJkYwRjEtSSRjb3NHNiQlKnByb3RlY3RlZEdGJTYjRjNGMUY0SSJDR0YmRjE3I0Ys

Maple d\303\241 a derivada como diff( ans3, x );

LCgqJiIiIyIiIilJInhHNiIiIiUhIiJGJSokKUYnI0YlRiRGJUYlKiYiIiRGJS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKDYjRidGJUYl

Como a derivada de nossa resposta \303\251 a fun\303\247\303\243o original, a antiderivada est\303\241 correta! Escrevemos isto como 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn = 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiM0YnL0Y5USdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0ZBLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlgtRkQ2LVEiL0YnRkFGR0ZKL0ZNRjdGTkZQRlJGVC9GV1EsMC4xNjY2NjY3ZW1GJy9GWkZqbi1GPjYkUSIyRidGQUZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GRDYtUSgmbWludXM7RidGQUZHRkpGTEZORlBGUkZUL0ZXUSwwLjIyMjIyMjJlbUYnL0ZaRmZvRj1GQy1GIzYmLUYsNiVRJGNvc0YnL0Y2RklGQS1GRDYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZBRkdGSkZMRk5GUEZSRlRGVkZZLUkobWZlbmNlZEdGJDYkLUYjNiRGMkZBRkFGQS1GRDYtUScmcGx1cztGJ0ZBRkdGSkZMRk5GUEZSRlRGZW9GZ28tRiw2JVEiQ0YnRjVGOEZB Note que se a constante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for omitida, teremos uma antiderivada. O mesmo seria verdade se um valor (value) espec\303\255fico fosse designado para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Quando dizemos a antiderivada, queremos dizer a fam\303\255lia de todas antiderivadas. Somente quando a constante for (is allowed to take) considerada entre todos os valores reais encontramos a antiderivada da fun\303\247\303\243o.

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique. with(RandomTools): randomize(): nn1 := Generate(integer(range=-5..5)): nn2 := Generate(integer(range=-15..15)): nn3 := Generate(integer(range=-5..5)): nn4 := Generate(integer(range=-15..15)): while (nn4=nn2) do nn4 := Generate(integer(range=-5..5)) od: nn5 := Generate(rational(range=0..1,denominator=20)): ff := nn1*Generate(choose([sin(x),cos(x),-sin(x),-cos(x)])): fn2 := nn2*x^nn3 + nn4*x^nn5 + ff: Fn2 := Int(fn2,x);

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJiokSSJ4R0YnIiIkISM6LUkkY29zR0YkNiNGKyEiJEYr

JSFH

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question. Avalie `$Fn2` (Sugest\303\243o#1: Use regras de antideriva\303\247\303\243o, se necess\303\241rio) (Sugest\303\243o#2: N\303\243o esque\303\247a da constante no final) JSFH

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed. value(Fn2)+C;

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region. evalb(`$ANSWER`-`$RESPONSE`=0);

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints. Use antiderivative rules, if necessary. Don't forget the constant at the end. Replace this text with hint 3. with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Use&MediumSpace;antiderivative&MediumSpace;rules,&MediumSpace;if&MediumSpace;necessary.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea1`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't&MediumSpace;forget&MediumSpace;the&MediumSpace;constant&MediumSpace;at&MediumSpace;the&MediumSpace;end.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response. Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea1`, `value`); ANSWER := value(Fn2)+C; if evalb(ANSWER-eval(parse(StudentResponse))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="&lt;NO RESPONSE&gt;"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect.&nbsp;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer:&nbsp;</mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>15</mn><mn>4</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mi mathvariant='normal'>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mfrac><mn>15</mn><mn>4</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mi>x</mi><mn>4</mn></msup></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><mi mathvariant='normal'>sin</mi><mo lspace='0.0em' rspace='0.0em'>&ApplyFunction;</mo><mfenced open='(' close=')' separators=','><mrow><mi>x</mi></mrow></mfenced></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

ATabela 21.4 resume os c\303\241lculos pelos quais a fam\303\255lia completa de antiderivadas determinadas por 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn \303\251 obtida. Primeiro, note que dt indica que t \303\251 a vari\303\241vel independente (independent variable) neste problema. Antes que as Regras de Antideriva\303\247\303\243o possam ser aplicadas a este problema, \303\251 necess\303\241rio expandir e simplificar o integrando. Os passos para encontrar todas as antiderivadas do integrando s\303\243o encontrados na Tabela 21.4. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Problema Original (Original Problem) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Expans\303\243o Alg\303\251brica (Algebraic Expansion) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Manipula\303\247\303\265es Alg\303\251bricas Adicionais (Additional Algebraic Manipulations) 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 Regras de Soma, Diferen\303\247a, M\303\272tiplo de Constante, e Pot\303\252ncia (Sum, Difference, Constant Multiple, and Power Rules) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjJGJ0YvLUZKNiRRIjVGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHRjQtSSNtaUdGJDYjUSFGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtRiw2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiNUYnL0Y5USdub3JtYWxGJy1JI21vR0YkNi1RMSZJbnZpc2libGVUaW1lcztGJ0ZBLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlgtRkQ2LVEiL0YnRkFGR0ZKL0ZNRjdGTkZQRlJGVC9GV1EsMC4xNjY2NjY3ZW1GJy9GWkZqbi1GPjYkUSIyRidGQUZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GRDYtUSgmbWludXM7RidGQUZHRkpGaG5GTkZQRlJGVEZpbkZbby1JJm1mcmFjR0YkNigtRj42JFEiNEYnRkEtRj42JFEiM0YnRkEvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmNwLyUpYmV2ZWxsZWRHRklGK0ZB 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 Simplifica\303\247\303\243o Alg\303\251brica Final (Final Algebraic Simplification) Tabela 21.4 Exemplo 21.4: Aplica\303\247\303\243o das Regras de Antideriva\303\247\303\243o a 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 Para confirmar este resultado, entre com a antiderivada como ans4 := 2/5*t^(5/2)-2*2/3*t^(3/2)+2*t^(1/2)+C;

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkklYW5zNEdGJiwqKiYjIiIjIiImIiIiKUkidEdGJiNGMEYvRjFGMSomIyIiJSIiJEYxKUYzI0Y4Ri9GMSEiIiomRi9GMSlGMyNGMUYvRjFGMUkiQ0dGJkYxNyNGLA==

E ent\303\243o, compute a derivada em rela\303\247\303\243o a t e simplifique para obter dF4 := diff( ans4, t ): dF4 = factor( value(dF4) );

LywoKiQpSSJ0RzYiIyIiJCIiIyIiIkYrKiZGKkYrKUYmI0YrRipGKyEiIiokRi1GL0YrKiYpLCZGJkYrRitGL0YqRitGLUYv

Resumindo, escrevemos ent\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEmJmludDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRC1JJm1mcmFjR0YkNigtRiM2Ji1JI21pR0YkNiNRIUYnLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYkLUYjNiYtRk02JVEidEYnLyUnaXRhbGljR0Y5L0YwUSdpdGFsaWNGJy1GLDYtUSgmbWludXM7RidGL0YyRjUvRjhGNEY6L0Y9RjRGPkZAL0ZDUSwwLjI3Nzc3NzhlbUYnL0ZGRl9vLUkjbW5HRiQ2JFEiMUYnRi9GL0YvLUZibzYkUSIyRidGLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGTEYvLUkmbXNxcnRHRiQ2I0ZYLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZjcC8lKWJldmVsbGVkR0Y0RkxGLw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjJGJ0YvLUZKNiRRIjVGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHRjQtSSNtaUdGJDYjUSFGJ0Yv 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

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique. with(RandomTools): randomize(): nn5 := Generate(integer(range=1..5)): nn6 := Generate(choose([2,3,4,5,10,15,20])): nn7 := Generate(rational(range=0..1,denominator=nn6)): xn := x^nn7; ff1 := sort(Generate(polynom(integer(range=0..20),x,degree=nn5)),x): fn3 := ff1/xn: Fn3 := Int(fn3,x); value(Fn3);

KiRJInhHNiIjIiIiIiIj

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LCQqJkkieEc2IiMiIiQiIiMsLCIlWz0iIiJGJCIlej8qJEYkRigiJChIKiRGJEYnIiRSJiokRiQiIiUiJF8jRisjRigiJCRw

JSFH

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question. Avalie `$Fn3` 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 (Sugest\303\243o #2: N\303\243o esque\303\247a de adicionar a constante no final) JSFH

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed. JSFHvalue(Fn3)+C; JSFH

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region. evalb(`$ANSWER`-`$RESPONSE`=0);

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints. Divide each term of the numerator by `$xn` Don't forget to add a constant at the end. Replace this text with hint 3. with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Divide&MediumSpace;each&MediumSpace;term&MediumSpace;of&MediumSpace;the&MediumSpace;numerator&MediumSpace;by&MediumSpace;</mtext><mtext></mtext><mrow><mrow><msqrt><mi>x</mi></msqrt></mrow></mrow><mtext></mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea2`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't&MediumSpace;forget&MediumSpace;to&MediumSpace;add&MediumSpace;a&MediumSpace;constant&MediumSpace;at&MediumSpace;the&MediumSpace;end.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response. Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea2`, `value`); ANSWER := value(Fn3)+C; if evalb(ANSWER-eval(parse(StudentResponse))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="&lt;NO RESPONSE&gt;"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect.&nbsp;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer:&nbsp;</mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mfrac><mn>2</mn><mn>693</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mi>x</mi><mrow><mn>3</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&amp;sol;</mo><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1848</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>2079</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>297</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>539</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>252</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>4</mn></msup></mrow></mrow></mfenced></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mfrac><mn>2</mn><mn>693</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mi>x</mi><mrow><mn>3</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&amp;sol;</mo><mn>2</mn></mrow></msup><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mfenced open='(' close=')' separators=','><mrow><mn>1848</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>2079</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mi>x</mi></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>297</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>539</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>252</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>4</mn></msup></mrow></mrow></mfenced></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

A Tabela 21.5 resume os c\303\241lculos pelos quais a fam\303\255lia completa de antiderivadas determinadas por 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn \303\251 obtida. N\303\243o tem muito que se possa fazer para reescrever o integrando desta integral indefinida em uma forma que as Regras de Antideriva\303\247\303\243o de Soma, Diferen\303\247a e de M\303\272ltiplo de Constante possam ser aplicadas. Mas, note que o coeficiente da raiz (root) quadrada \303\251 exatamente a derivada da express\303\243o dentro da raiz quadrada. Este \303\251 o padr\303\243o que deve ser usado para a Regra de Pot\303\252ncia Generalizada com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNictRiw2JVEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y6USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZTLUYjNiYtRj02LVEiKEYnRkAvRkNGOEZFL0ZIRjhGSUZLRk1GTy9GUlEsMC4xNjY2NjY3ZW1GJy9GVUZobi1GIzYkLUYsNiVRInhGJ0Y2RjlGQC1GPTYtUSIpRidGQEZlbkZFRmZuRklGS0ZNRk9GZ24vRlVRLDAuMTExMTExMWVtRidGQEYrRkAtRj02LVEiPUYnRkBGQkZFRkdGSUZLRk1GTy9GUlEsMC4yNzc3Nzc4ZW1GJy9GVUZoby1GIzYpRistRiM2JkYrLUklbXN1cEdGJDYlRlxvLUkjbW5HRiQ2JFEiNUYnRkAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGQC1GPTYtUSIrRidGQEZCRkVGR0ZJRktGTUZPL0ZSUSwwLjIyMjIyMjJlbUYnL0ZVRlxxLUYjNiZGKy1GX3A2JUZcby1GYnA2JFEiMkYnRkBGZXBGK0ZARmhwRmJxRkBGK0ZARitGQA== e 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. O conjunto completo de passos para encontrar a antiderivada \303\251 encontrado na Tabela 21.5. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Problema Original (Original Problem) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Substitui\303\247\303\243o (Substitution): 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 Regra de Pot\303\252ncia Generalizada (Generalized Power Rule), 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 Inverter a Substitui\303\247\303\243o (Reverse the Substitution) Tabela 21.5 Exemplo 21.5: Aplica\303\247\303\243o das Regras de Antideriva\303\247\303\243o aLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RidGNEY3Rj5GPkY+LUY7Ni1RIj1GJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGam4tRiM2KEYrLUYjNiYtRjs2LVEiKEYnRj4vRkFGNkZDL0ZGRjZGR0ZJRktGTS9GUFEsMC4xNjY2NjY3ZW1GJy9GU0Zmby1GIzYoRistRiM2Jy1JI21uR0YkNiRRIjVGJ0Y+LUY7Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSLUYjNiZGKy1JJW1zdXBHRiQ2JUZZLUZdcDYkUSI0RidGPi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y+RitGPi1GOzYtUSIrRidGPkZARkNGRUZHRklGS0ZNL0ZQUSwwLjIyMjIyMjJlbUYnL0ZTRmJxLUYjNiYtRl1wNiRRIjJGJ0Y+RmBwRllGPkYrRj4tRjs2LVEiKUYnRj5GY29GQ0Zkb0ZHRklGS0ZNRmVvL0ZTUSwwLjExMTExMTFlbUYnRj5GYHAtSSZtc3FydEdGJDYjLUYjNilGKy1GIzYmRistRmZwNiVGWUZccEZbcUYrRj5GXnEtRiM2JkYrLUZmcDYlRllGZnFGW3FGK0Y+Rl5xRmZxRj5GK0Y+RitGPg== Note que a constante aparece no problema quando o sinal de integral desaparece, e que aparece isolada das outras express\303\265es Como anteriormente, este resultado, que entrou como ans5 := 2/3*(x^5+x^2+2)^(3/2)+C;

LV9JLFR5cGVzZXR0aW5nR0koX3N5c2xpYkc2IkksbXByaW50c2xhc2hHRiY2JDcjPkklYW5zNUdGJiwmKiYjIiIjIiIkIiIiKSwoKiQpSSJ4R0YmIiImRjFGMSokKUY2Ri9GMUYxRi9GMSNGMEYvRjFGMUkiQ0dGJkYxNyNGLA==

pode ser confirmado pela deriva\303\247\303\243o, que o Maple d\303\241 como diff( ans5, x );

KiYpLCgqJClJInhHNiIiIiYiIiJGKiokKUYnIiIjRipGKkYtRiojRipGLUYqLCYqJkYpRiopRiciIiVGKkYqKiZGLUYqRidGKkYqRio=

\303\223timo! Isto mostra que 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

Using the Maple-graded question type, you create a question that uses Maple functionality when creating the correct answer and determining if the student's response is correct. The Maple-graded question type has an option to plot the student's response. To include the plot option, insert the corresponding task template. For information on creating questions, making assignments, and exporting Maple T.A. course modules, see Overview of Maple T.A. Integration.

Algorithmic variables can be used to create a question that contains randomly generated parameters. You can refer to algorithmic variables in the Question, Answer, Hints, and Feedback input regions, as well as in other variable definitions. To reference an algorithmic variable, include "`$variable`" as text or 2-D Math, for example, x := `$myvariable`. Adding algorithmic variables to the question is optional. In the following execution group, add an algorithmic variable. To include more variables, add more execution groups. If your assignment contains more than one algorithmic variable, ensure the variable names are unique. with(RandomTools): randomize(): nn8 := Generate(integer(range=3..5)): nn9 := Generate(choose([2,3,4,5,10,20])): nn10 := Generate(rational(range=0..1,denominator=nn9)): ff2 := sort(Generate(polynom(integer(range=-10..10),x,degree=nn8)),x): fn4 := diff(ff2,x)*(ff2)^nn10: Fn4 := Int(fn4,x); value(Fn4);

LUkkSW50RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJiwsKiRJInhHRiciIiUiI0QqJEYsIiIkIiM3KiRGLCIiIyEjN0YsISIpISIiIiIiRjcsLiokRiwiIiZGOkYrRjBGLyEiJUYyRjtGLEY2IiIoRjcjRjciIzVGLA==

LCQqJCwuKiRJInhHNiIiIiZGKCokRiYiIiUiIiQqJEYmRishIiUqJEYmIiIjRi1GJiEiIiIiKCIiIiMiIzYiIzUjRjVGNA==

JSFH

The question can contain text, 2-D Math, plots, images, and algorithmic variables. To insert a plot in the question, use the Plot Component. In the following text region, enter the full contents of the question. Avalie `$Fn4` (Sugest\303\243o#1:Veja se uma fun\303\247\303\243o \303\251 derivada da outra, e fa\303\247a uma substitui\303\247\303\243o.) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJ0YrLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw==(Sugest\303\243o#2:N\303\243o esque\303\247a da constante no final) JSFH

To evaluate a student's response, enter the correct answer. Complete each line of code with a semicolon. The last line must evaluate to an expression that will be stored as the variable `$ANSWER`. Enter Maple code in 1-D Math that evaluates to the correct answer. Add additional execution groups as needed. value(Fn4)+C; JSFH

To evaluate a student's response, you must evalute to a Boolean value (true or false). The variable `$RESPONSE` is automatically initialized to the student's response. Using `$ANSWER` (the correct answer) and `$RESPONSE` (the student response), one example of evaluating to a Boolean value is, evalb(`$ANSWER`-`$RESPONSE`=0); Enter Maple code to evaluate a student's response. To add additional Maple functionality, use the Answer input region. evalb(`$ANSWER`-`$RESPONSE`=0);

A question can offer hints to students when requested. Hints can contain text, 2-D Math, and algorithmic variables. Adding hints to the question is optional. Enter your hints in the following table. You can provide up to three hints. See whether one function is the derivative of the other, and make a substitution. Don't forget about the constant at the end. Replace this text with hint 3. with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>See&MediumSpace;whether&MediumSpace;one&MediumSpace;function&MediumSpace;is&MediumSpace;the&MediumSpace;derivative&MediumSpace;of&MediumSpace;the&MediumSpace;other,&MediumSpace;and&MediumSpace;make&MediumSpace;a&MediumSpace;substitution.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet); with(StringTools): with(DocumentTools): response := GetProperty(`TextArea3`, `value`); if response = `` then response := "</mtext><mtext>&lt;NO RESPONSE&gt;</mtext><mtext>"; fi; hint := SubstituteAll("<math><mrow><mtext>Don't&MediumSpace;forget&MediumSpace;about&MediumSpace;the&MediumSpace;constant&MediumSpace;at&MediumSpace;the&MediumSpace;end.</mtext><mtext>&NewLine;</mtext></mrow></math>", "`\134$RESPONSE`", response); with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Hint", [[MathMLViewer('value' = hint, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): Maplets[Display](maplet);

A question can display feedback when a student provides an incorrect response. The feedback can contain text, 2-D Math, and algorithmic variables. The feedback can also refer to `$RESPONSE` (the student response) and `$ANSWER` (the correct answer). Adding feedback to the question is optional. In the following text region, enter feedback to an incorrect response. Replace this text with feedback.

with(StringTools): with(DocumentTools): feedback:=""; StudentResponse := GetProperty(`TextArea3`, `value`); ANSWER := value(Fn4)+C; if evalb(ANSWER-eval(parse(StudentResponse))=0) then feedback:=cat("<math><mrow><mtext mathvariant='bold'>Correct!&NewLine;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext></mrow></math>"); else if StudentResponse = "" then StudentResponse:="&lt;NO RESPONSE&gt;"; fi; feedback:=cat("<math><mrow><mtext mathvariant='bold'>Your answer is incorrect.&nbsp;</mtext><mtext>&NewLine;</mtext><mtext mathvariant='bold'>Your Answer:&nbsp;</mtext><mtext>", StudentResponse, "</mtext><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, "<mtext mathvariant='bold'>Correct Answer:&nbsp;</mtext><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mfrac><mn>10</mn><mn>11</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mn>7</mn></mrow></mfenced><mrow><mn>11</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&amp;sol;</mo><mn>10</mn></mrow></msup></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math><mtext>&NewLine;</mtext>"); feedback:=cat(feedback, SubstituteAll("<mrow><mtext>&NewLine;</mtext></mrow>", "`$RESPONSE`", StudentResponse)); feedback:=SubstituteAll(feedback, "`$ANSWER`", "<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mrow><mrow><mfrac><mn>10</mn><mn>11</mn></mfrac><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><mrow><msup><mfenced open='(' close=')' separators=','><mrow><mrow><mn>5</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>5</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mrow><mn>3</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>4</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>3</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mrow><mn>4</mn><mo lspace='0.0em' rspace='0.0em'>&InvisibleTimes;</mo><msup><mi>x</mi><mn>2</mn></msup></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>x</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mn>7</mn></mrow></mfenced><mrow><mn>11</mn><mo lspace='0.1666667em' rspace='0.1666667em' stretchy='true'>&amp;sol;</mo><mn>10</mn></mrow></msup></mrow></mrow><mo lspace='0.2222222em' rspace='0.2222222em'>&amp;plus;</mo><mi>C</mi></mrow></mrow></mstyle></math>"); feedback:=cat(feedback, "</mrow></math>"); fi; with(Maplets[Elements]): maplet := Maplet(Window('title' = "Maple TA Feedback", [[MathMLViewer('value' = feedback, 'fontsize'='12', 'width'='600', 'height'='200', 'breakwidth'='600')], [Button("OK", Shutdown())]])): if feedback <> "" then Maplets[Display](maplet); fi;

A Tabela 21.6 resume os c\303\241lculos pelos quais a fam\303\255lia completa de antiderivadas determinadas por 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn \303\251 obtida. Compare este integrando com o integrando no Exemplo 21.4. Note que expandindo o denominador (denominator) do integrando n\303\243o ajuda a encontrar a antiderivada. Em vez disto, deve ser notado que se o numerador (numerator) fosse LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZNLUYsNiVRInpGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNlEnaXRhbGljRidGNUYrRjU= seria ent\303\243o a derivada de of 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. Escrevendo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiQtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjgtRiM2JkYrLUYjNiZGKy1JJW1zdXBHRiQ2JS1GIzYmLUkjbW9HRiQ2LVEiKEYnRjgvJSZmZW5jZUdRJXRydWVGJy8lKnNlcGFyYXRvckdRJmZhbHNlRicvJSlzdHJldGNoeUdGSi8lKnN5bW1ldHJpY0dGTS8lKGxhcmdlb3BHRk0vJS5tb3ZhYmxlbGltaXRzR0ZNLyUnYWNjZW50R0ZNLyUnbHNwYWNlR1EsMC4xNjY2NjY3ZW1GJy8lJ3JzcGFjZUdGWi1GIzYnRistRiM2JkYrLUZANiUtRiw2JVEiekYnLyUnaXRhbGljR0ZKL0Y5USdpdGFsaWNGJy1GNTYkUSIyRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0Y4LUZFNi1RIitGJ0Y4L0ZJRk1GSy9GT0ZNRlBGUkZURlYvRllRLDAuMjIyMjIyMmVtRicvRmZuRmBwRjRGOC1GRTYtUSIpRidGOEZIRktGTkZQRlJGVEZWRlgvRmZuUSwwLjExMTExMTFlbUYnRjhGZG9GZ29GK0Y4RitGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHEvJSliZXZlbGxlZEdGTUYrRjg= com um expoente negativo (negative) , a Regra de Pot\303\252ncia Generalizada tpoderia ser usada para avaliar esta integral indefinida. A avalia\303\247\303\243o completa aparece na Tabela 21.6. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn JSFH Problema Original (Original Problem) 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Reescrito Alg\303\251brico: expoente negativo (Algebraic Rewrite: negative exponent) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0YvLUZKNiRRIjJGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHRjQtSSNtaUdGJDYjUSFGJ0Yv 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Multiplicar por (Multiply by)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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0YvLUZKNiRRIjJGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHRjQtSSNtaUdGJDYjUSFGJ0Yv 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjZHpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn Substitui\303\247\303\243o (Substitution): 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZDLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJ0YvLUZKNiRRIjJGJ0YvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZVLyUpYmV2ZWxsZWRHRjQtSSNtaUdGJDYjUSFGJ0Yv LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSZtZnJhY0dGJDYoLUYjNiZGKy1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2Ji1GIzYmRistRiM2Ji1GLDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRkVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZPLyUpc3RyZXRjaHlHRk8vJSpzeW1tZXRyaWNHRk8vJShsYXJnZW9wR0ZPLyUubW92YWJsZWxpbWl0c0dGTy8lJ2FjY2VudEdGTy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmhuLUY4NiQtRiM2JC1GLDYlUSJ6RidGQUZERktGS0ZLRitGS0ZLLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUYjNiUtRkg2LVEoJm1pbnVzO0YnRktGTUZQRlJGVEZWRlhGWi9GZ25RLDAuMjIyMjIyMmVtRicvRmpuRl5wLUkjbW5HRiQ2JFEiMUYnRktGSy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGK0ZLRmhvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZccS8lKWJldmVsbGVkR0ZPLUZINi1RJyZwbHVzO0YnRktGTUZQRlJGVEZWRlhGWkZdcEZfcC1GLDYlUSJDRidGQUZERks= Regra de Pot\303\252ncia Generalizada (Generalized Power Rule), LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk= 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 Inverter a Substitui\303\247\303\243o (Reverse the Substitution) 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 Manipula\303\247\303\243o Alg\303\251brica (Algebraic Manipulation) Tabela 21.6 Exemplo 21.6: Aplica\303\247\303\243o das Regras de Antideriva\303\247\303\243o a 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

O processo de desfazer a deriva\303\247\303\243o \303\251 chamado de antideriva\303\247\303\243o ou integra\303\247\303\243o indefinida. Como a derivada de uma constante \303\251 zero, isto \303\251, como 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, se uma antiderivada pode ser encontrada, ao adicionar uma constante arbitr\303\241ria produz uma fam\303\255lia infinita de antiderivadas. As regra de Antideriva\303\247\303\243o s\303\243o obtidas invertendo uma Regra de Deriva\303\247\303\243o. Uma boa propriedade das antiderivadas \303\251 que \303\251 sempre poss\303\255vel usar deriva\303\247\303\243o para verificar que uma antiderivada est\303\241 correta.

A habilidade para encontrar antiderivadas e avaliar integrais indefinidas \303\251 fundamental para as duas unidades finais deste curso. O maplet Antiderivada (Antiderivative maplet) pode auxiliar em seu desenvolvimento de uma melhor compreens\303\243o da rela\303\247\303\243o geom\303\251trica entre uma fun\303\247\303\243o e suas antiderivadas. Use a sess\303\243o pr\303\241tica online para este cap\303\255tulo para melhorar suas habilidades. O pr\303\263ximo cap\303\255tulo aplica a procura por antiderivadas para investigar solu\303\247\303\265es (solutions) de Equa\303\247\303\265es Diferenciais (Differential Equations). Este cap\303\255tulo \303\251 uma breve introdu\303\247\303\243o para um importante t\303\263pico em matem\303\241tica. Muitos de voc\303\252s provavelmente tomar\303\243o um curso em Equa\303\247\303\265es Diferenciais depois de completar a seq\303\274\303\252ncia em C\303\241lculo.

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