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Homework Help: Calculate the integral of x^2 e^(-x^2) from -infinity to + infinity

  1. Oct 3, 2006 #1
    [tex] \frac{1}{\sqrt{2 \pi \sigma^2}} \int_{-\infty}^{\infty} x^2 e^{\frac{-x^2}{2 \sigma^2}} dx [/tex]
    I think just slving this would be fine too

    [tex] \int_{-\infty}^{\infty} x^2 e^{-x^2} dx [/tex]

    what is the trick to solving this?/

    Cnat integrate by parts because that would yeild Erf function which i have no been taught

    I was told that there was some trick to differentiate both sides by sigma... but im not relly sure...?
  2. jcsd
  3. Oct 3, 2006 #2


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    Homework Helper

    You know:

    [tex]\int_{-\infty}^\infty e^{-\sigma x^2} dx = \sqrt{\frac{\pi}{\sigma}} [/tex]

    Differentiate both sides with respect to sigma.
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