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Integral of x^2e^(-x^2)

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Use the fact that the integral evaluated from -∞ to +∞ of e^(-x^2) is sqrt(∏) to evaluate the integral from -∞ to +∞ of x^2(e^(-x^2)).


    2. Relevant equations



    3. The attempt at a solution

    I tried using integration by parts and I came down to an indefinite integral of sqrt(∏)*x^2. I know the answer is sqrt(∏)/2 but I don't see how. Can someone tell me what im doing wrong please.
     
  2. jcsd
  3. Apr 16, 2012 #2

    That doesn't seem right. Try doing integration by parts by setting [itex]u = x \text{ and } dv=xe^{-x^2}dx[/itex].
     
  4. Apr 16, 2012 #3
    Thanks I got the answer using that method
     
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