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Thread: integration

  1. #1
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    integration

    $\displaystyle
    \int^{\infty}_{0}x^{2}e^{-x^2/2}dx$
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  2. #2
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    $\displaystyle \int^{\infty}_{0}x^{2}e^{-x^2/2}dx$
    $\displaystyle =\int^{\infty}_{0}x.xe^{-x^2/2}dx$
    $\displaystyle =[-xe^{-x^{2}/2}]_{0}^{\infty}+\int^{\infty}_{0}e^{-x^2/2}dx$
    $\displaystyle =0+\int^{\infty}_{0}e^{-x^2}\sqrt{2}dx$
    $\displaystyle =\sqrt{\frac{\pi}{2}}$
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