- #1
Lancelot59
- 646
- 1
This is the problem:
[tex]\int_{-\infty}^{\infty} {xe^{-x^{2}}dx}[/tex]
I noticed the function was even, so I then did this:
[tex]2\int_{0}^{\infty} {xe^{-x^{2}}dx}[/tex]
I attempted to do integration by parts:
[tex]u=e^{-x^{2}}, du=-2e^{-x^{2}}, dv=x, v=\frac{x^{2}}{2}[/tex]
which still left me with this at the end:
(I left out the bounds)
[tex]\frac{x^{2}}{2}(e^{-x^{2}} - \int_{}^{} {e^{-x^{2}}dx})[/tex]
and of course that integral can't be done. Doing parts the other way results with the same issue, and I don't see how a substitution could work. Thanks in advance for any help.
[tex]\int_{-\infty}^{\infty} {xe^{-x^{2}}dx}[/tex]
I noticed the function was even, so I then did this:
[tex]2\int_{0}^{\infty} {xe^{-x^{2}}dx}[/tex]
I attempted to do integration by parts:
[tex]u=e^{-x^{2}}, du=-2e^{-x^{2}}, dv=x, v=\frac{x^{2}}{2}[/tex]
which still left me with this at the end:
(I left out the bounds)
[tex]\frac{x^{2}}{2}(e^{-x^{2}} - \int_{}^{} {e^{-x^{2}}dx})[/tex]
and of course that integral can't be done. Doing parts the other way results with the same issue, and I don't see how a substitution could work. Thanks in advance for any help.