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fast_eddie1103
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Can someone pls show me a method for evaluating the integral of (2x^2)exp(-x^2) dx with limits from 0 to infinity, knowing that the integral of exp(-x^2) dx with the same limits is 1/2 pi^1/2

thank you
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yusufu
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Report 12 years ago
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(Original post by fast_eddie1103)
Can someone pls show me a method for evaluating the integral of (2x^2)exp(-x^2) dx with limits from 0 to infinity, knowing that the integral of exp(-x^2) dx with the same limits is 1/2 pi^1/2

thank you
integration by parts:

u = x v' = 2xe-x2
u' = 1 v = -e-x2


INT (2x^2)e-x2 dx = [-xe-x2] (between 5 and 0) - INT -e-x2 dx
=[-xe-x2] (between 5 and 0) + INT e-x2 dx
= [-xe-x2] (between 5 and 0) + 1/2 pi^1/2
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