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## Homework Statement

Given that:

[tex]\oint[/tex] e

^{-ax^2}dx = [tex]\sqrt{}\pi/a[/tex] (between infinity and minus infinity)

show that

[tex]\oint[/tex]x

^{2}e

^{-ax^2}dx = 1/4[tex]\sqrt{}\pi/a^3[/tex] (between 0 and infinity)

## Homework Equations

## The Attempt at a Solution

I assume integration by parts may be necessary, but not really sure how to go about it, ie. what is first expression really telling you as the limits are different to the second. I think it might also be the infinities confusing me so if someone could point me in the right direction that'd be appreciated.