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

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spaniks
#1
Apr16-12, 12:56 PM
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.
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scurty
#2
Apr16-12, 02:41 PM
P: 392
Quote Quote by spaniks View Post
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 [itex]u = x \text{ and } dv=xe^{-x^2}dx[/itex].
spaniks
#3
Apr16-12, 02:48 PM
P: 6
Thanks I got the answer using that method


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