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Probability - u substitution to find gamma function.

  1. Dec 14, 2011 #1
    1. The problem statement, all variables and given/known data

    [itex]\int_0^∞ x^2exp(-x/2) dx[/itex]

    2. Relevant equations

    afe9f86ae39cdf0260aad124aac4a3e9.png

    3. The attempt at a solution

    Using u substitution:

    u = x/2
    du = 1/2 dx

    [itex]\int_0^∞ 4u^2exp(-u) du*2[/itex]
    = 8 [itex]\Gamma(3)[/itex]
    = 8*3!
    = 48

    But the correct answer is 16 when I plug it in Wolfram's definite integral calculator. I don't see where's my mistake?

    Thank you very much!
     
  2. jcsd
  3. Dec 14, 2011 #2
    Wow, Gamma(3) = 2!, not 3!. Silly me! Thanks anyways.
     
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