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Math Help - integration

  1. #1
    Junior Member
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    integration

    <br />
\int^{\infty}_{0}x^{2}e^{-x^2/2}dx
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  2. #2
    Senior Member
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    \int^{\infty}_{0}x^{2}e^{-x^2/2}dx
    =\int^{\infty}_{0}x.xe^{-x^2/2}dx
    =[-xe^{-x^{2}/2}]_{0}^{\infty}+\int^{\infty}_{0}e^{-x^2/2}dx
    =0+\int^{\infty}_{0}e^{-x^2}\sqrt{2}dx
    =\sqrt{\frac{\pi}{2}}
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