Hey, i've been learning about gaussian integrals lately. And i'm now stuck in one part. I am now trying to derive some kind of general formula for gaussian integrals(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int x^n e^{-\alpha x^2} [/tex]

for the case where n is even. So they ask me to evaluate the special case n=0 and alpha=1. So its [tex] I= \int^{\infty}_{-\infty} e^{-x^2} dx [/tex]. When i square this integral, they said that its [tex] I^2= ({\int^{\infty}_{-\infty} e^{-x^2} dx})({\int^{\infty}_{-\infty} e^{-y^2} dy}) [/tex] with both x and y as according to them, i have to use a different variable for the first and second integral factors.

Why is this so? I have limited calc background. So i was wondering you guys could help me out. Thanks alot.....

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# Problem with a gaussian integral.

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