Integrais O Maple pode calcular muitas integrais definidas e indefinidas, de modo anal\303\255tico, como aquelas que constam dos livros textos de c\303\241lculo. O Maple tamb\303\251m calcula integrais definidas atrav\303\251s de m\303\251todos num\303\251ricos. Dentro da biblioteca student do Maple, podemos encontrar maneiras de simular, passo a passo, os m\303\251todos cl\303\241ssicos de integra\303\247\303\243o que est\303\243o nos textos de c\303\241lculo tais como : substitui\303\247\303\243o, integra\303\247\303\243o por partes e fra\303\247\303\265es parciais. Calculamos a integral definda da express\303\243o alg\303\251brica f(x) no intervalo [a,b] com int( f(x) , x=a .. b) e a integral indefinida da express\303\243o f(x) com int( f(x), x ) O argumento da integral deve ser uma express\303\243o alg\303\251brica . ( N\303\243o podemos tomar f como cos , sem a vari\303\241vel x, pois int n\303\243o \303\251 um operador sobre fun\303\247\303\265es como o operador D de deriva\303\247\303\243o) 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 \303\251 inerte e retorna a express\303\243o matem\303\241tica da integral LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkjbWlHRiQ2JVEkSW50RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNi8tRiw2JVEkc2luRicvRjBRJmZhbHNlRicvRjNRJ25vcm1hbEYnLUY2NiQtRiM2JS1GLDYlUSJ4RidGL0YyLyUrZXhlY3V0YWJsZUdGPkY/Rj8tSSNtb0dGJDYtUSIsRidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUZLNi1RIn5GJ0Y/Rk4vRlFGPkZSRlRGVkZYRlpGZm4vRmpuRmhuRkUtRks2LVEiPUYnRj9GTkZfb0ZSRlRGVkZYRlovRmduUSwwLjI3Nzc3NzhlbUYnL0ZqbkZlby1JI21uR0YkNiRRIjBGJ0Y/LUZLNi1RIy4uRidGP0ZORl9vRlJGVEZWRlhGWi9GZ25RLDAuMjIyMjIyMmVtRidGYG8tRiw2JVEjUGlGJ0Y9Rj8tRks2LVEiL0YnRj9GTkZfby9GU0YxRlRGVkZYRlovRmduUSwwLjE2NjY2NjdlbUYnL0ZqbkZocC1GaG82JFEiMkYnRj9GSEY/Rj8tRks2LVEiO0YnRj9GTkZQRlJGVEZWRlhGWkZmbkZmb0Zcby1GLDYlUShyZXRvcm5hRidGL0YyRlxvLUYsNiVRImFGJ0YvRjJGXG8tRiw2JVEvZXhwcmVzcyYjMjI3O29GJ0YvRjJGXG8tRiw2JVEwbWF0ZW0mIzIyNTt0aWNhRidGL0YyRlxvLUYsNiVRI2RhRidGL0YyRlxvLUYsNiVRKWludGVncmFsRidGL0YyRkhGPw== value(Int (f (x) , x=a..b) Podemos efetuar a opera\303\247\303\243o dada por Int com 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 A integral da distibui\303\247\303\243o gaussiana \303\251 dada pela fun\303\247\303\243o erro erf(x). Por exemplo 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 Muitas integrais podem ter respostas em termos de fun\303\247\303\265es internas do Maple tais como erf(x) , Bessel, Gamma etc A integra\303\247\303\243o num\303\251rica de f(x) no intervalo [a,b] \303\251 efetuadada com evalf( Int ( f(x), x=a..b ) ) Se queremos optar por uma precis\303\243o num\303\251rica de n d\303\255gitos ou por um dos m\303\251todos num\303\251ricos usamos as op\303\247\303\265es evalf( Int ( f(x), x=a..b , Precis\303\243o, \010M\303\251todo ) ) na qual Precis\303\243o \303\251 um inteiro e M\303\251todo \303\251 o nome do m\303\251todo usado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2KC1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1GLDYlUSRJbnRGJ0YvRjItRjY2JC1GIzY1LUYsNiVRJHNpbkYnL0YwRkJGPi1GNjYkLUYjNiUtRiw2JVEieEYnRi9GMi8lK2V4ZWN1dGFibGVHRkJGPkY+LUY7Ni1RIixGJ0Y+RkAvRkRGMUZFRkdGSUZLRk1GTy9GU1EsMC4zMzMzMzMzZW1GJ0Y6Rl1vLUY7Ni1RIj1GJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGXHAtSSNtbkdGJDYkUSIwRidGPi1GOzYtUSMuLkYnRj5GQEZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJ0ZSLUYsNiVRI1BpRidGaG5GPi1GOzYtUSIvRidGPkZARkMvRkZGMUZHRklGS0ZNL0ZQUSwwLjE2NjY2NjdlbUYnL0ZTRl9xLUZfcDYkUSIyRidGPkZib0Y6LUZfcDYkUSMxMEYnRj5GYm8tRiw2JVEoX0NDcXVhZEYnRi9GMkY6RmBvRj5GPkY6RmBvRj5GPi1GOzYtUSI7RidGPkZARmVvRkVGR0ZJRktGTUZPRl1wRmBvRj4= O m\303\251todo utilizado, por default, \303\251 o Clenshaw-Curtise que \303\251 denotado por _CCquad . Existem dois outros m\303\251todos dispon\303\255veis _Dexp e _NCrule , ver no help on line evalfint. . Veja no help o uso dos seguintes comandos utilizados relacinados com integra\303\247\303\243o student[changevar] faz mudan\303\247a de vair\303\241vel student[intparts] faz integral por partes convert/parfrac converte em fra\303\247\303\265es parciais Outros comandos da biblioteca student[ ] relacionados com integral s\303\243o leftbox, leftsum, midlebox, midlesum, rightbox, rightsum, simpson, trapezoid. Sintaxe dos comandos utilizados 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 JSFH