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How do you find the integral of #int (x^2)(e)^(-x^3) dx# from negative infinity to infinity?

1 Answer

Sep 26, 2015

#+oo#

Explanation:

#-x^3=t => -3x^2dx=dt => x^2dx=-dt/3#

#int x^2e^(-x^3)dx=-1/3inte^tdt=-1/3e^(-x^3)+C#

#I=int_-oo^(+oo) x^2e^(-x^3)dx= -1/3e^(-x^3)|_-oo^(+oo)#

#I=-1/3lim_(x->+oo) e^(-x^3) + 1/3lim_(x->-oo) e^(-x^3)#

#I=0+oo=+oo#

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