This should be a fairly simple integral but I can't get it for some reason. Here's the problem:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A\int_{-\infty}^{\infty} x e^{-\lambda(x-a)^2}dx[/tex]

Now I know that

[tex]\int_{-\infty}^{\infty} e^{-x^2}dx=\sqrt{\pi}[/tex]

only for those limits.

Okay so I do parts,

[tex]u=x[/tex]

[tex]du=dx[/tex]

[tex]dv=e^{-\lambda(x-a)^2}dx[/tex]

[tex]v=?[/tex]

When you evaluate the integral from dv to get v, you substitue say

[tex]s=\sqrt{\lambda}(x-a)[/tex]

to make it like the second integral i put down, but you can't evaluate it between the limits of -infinity to infinity when doing parts right? And the indefinite integral of this form is not solvable as far as I know.

BTW, This is for my QM class, finding the average/expectation value of x,

[tex]<x>[/tex]

Am I even going about this the right way? I don't know anymore. Please tell me where I screwed up and point me in the right direction.

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# Homework Help: Simple integral or not?

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