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

1. Apr 16, 2012

### spaniks

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. Apr 16, 2012

### scurty

That doesn't seem right. Try doing integration by parts by setting $u = x \text{ and } dv=xe^{-x^2}dx$.

3. Apr 16, 2012

### spaniks

Thanks I got the answer using that method