(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

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

3. 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?

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# Homework Help: Prove the improper triple integral equals 2*Pi

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