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

Integrate:

[tex]\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-2\sqrt{x^2+y^2+z^2}}dxdydz[/tex]

hint: use spherical integration

2. Relevant equations

[tex]p=\sqrt{x^2+y^2+z^2}[/tex]

[tex]dV=dp d\phi p sin\phi p d\theta[/tex]

3. The attempt at a solution

[tex]\int_{0}^{\infty}\int_{0}^{\pi}\int_{0}^{2\pi}e^{-2p} p^2 sin\phi d\theta d\phi dp[/tex]

look at integration for p since it is the most hard one first:

Integration by parts:

[tex]sin\phi\int_{0}^{\infty}e^{-2p} p^2 dp[/tex]

[tex]\int_{0}^{\infty}e^{-2p} p^2 dp=[\frac{e^{-2p}}{-2} p^2+\int_{0}^{\infty}e^{-2p}pdp]^{\infty}_0[/tex] (I)

[tex]\int_{0}^{\infty}e^{-2p}pdp=[\frac{e^{-2p}}{-2}p+\int_{0}^{\infty}e^{-2p}dp]^{\infty}_0=[\frac{e^{-2p}}{-2}p+\frac{e^{-2p}}{-2}]^{\infty}_0[/tex]

and (I) becomes:

[tex][\frac{e^{-2p}}{-2} p^2+\frac{e^{-2p}}{-2}p+\frac{e^{-2p}}{-2}]^{\infty}_0[/tex]

but here i get infinity in numerator and denumerator for [tex]p=\infty[/tex]. How do I solve this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integrating problem

**Physics Forums | Science Articles, Homework Help, Discussion**