- #1
Zacarias Nason
- 68
- 4
Hey, folks. I'm doing a problem wherein I have to evaluate a slight variation of the Gaussian integral for the first time, but I'm not totally sure how to go about it; this is part of an integration by parts problem where the dv is similar to a gaussian integral:
[tex] \int_{-\infty}^{\infty}x^2e^{-\alpha x^2} dx, \ \text{where} \ \alpha > 0 [/tex]. My question is, how should I deal with the alpha in the exponent? I know the Gaussian integral equals
[tex] \sqrt{\pi}[/tex]
But how do I deal with that alpha?
I thought I found my answer in a handout, but when I applied it, I ended up still being wrong; I attempted to integrate by parts and I got zero, the two terms cancelling each other out; what gives?
[tex] \int_{-\infty}^{\infty}x^2e^{-\alpha x^2} dx, \ \text{where} \ \alpha > 0 [/tex]. My question is, how should I deal with the alpha in the exponent? I know the Gaussian integral equals
[tex] \sqrt{\pi}[/tex]
But how do I deal with that alpha?
I thought I found my answer in a handout, but when I applied it, I ended up still being wrong; I attempted to integrate by parts and I got zero, the two terms cancelling each other out; what gives?
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