How to Evaluate the Integral of x^2e^(-x^2) Using the Integral of e^(-x^2)

[spaniks]

Homework Statement

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)).

Homework Equations

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 I am doing wrong please.

 

[scurty]

Homework Statement

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)).

Homework Equations

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 I am doing wrong please.

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

 

[spaniks]

Thanks I got the answer using that method