# Homework Help: Probability - u substitution to find gamma function.

1. Dec 14, 2011

### sirhc1

1. The problem statement, all variables and given/known data

$\int_0^∞ x^2exp(-x/2) dx$

2. Relevant equations

3. The attempt at a solution

Using u substitution:

u = x/2
du = 1/2 dx

$\int_0^∞ 4u^2exp(-u) du*2$
= 8 $\Gamma(3)$
= 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. Dec 14, 2011

### sirhc1

Wow, Gamma(3) = 2!, not 3!. Silly me! Thanks anyways.