- #1
PICsmith
- 54
- 0
This should be a fairly simple integral but I can't get it for some reason. Here's the problem:
[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.
[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.