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

by spaniks
Tags: integration, integration by parts
 P: 6 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.
P: 272
 Quote by 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.

That doesn't seem right. Try doing integration by parts by setting $u = x \text{ and } dv=xe^{-x^2}dx$.
 P: 6 Thanks I got the answer using that method

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