- #1

alanthreonus

- 10

- 0

## Homework Statement

Show that

[tex]\int^{infinity}_{-infinity}\int^{infinity}_{-infinity}\int^{infinity}_{-infinity}sqrt(x^2+y^2+z^2)e^-^(^x^2^+^y^2^+^z^2^)dxdydz = 2\pi[/tex]

## Homework Equations

[tex]x^2+y^2+z^2 = \rho^2 [/tex]

## The Attempt at a Solution

I converted to spherical coordinates to get

[tex]\int^{2\pi}_{0}\int^{2\pi}_{0}\int^{infinity}_{0}\rho^3e^-^\rho^2sin\phi d\rho d\phi d\theta[/tex]

But I don't think I can integrate that. Am I approaching this the right way?