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

Evaluate [tex]\int\int\int[/tex] 1/[tex]\sqrt{x^{2}+y^{2}+z^{2}+3}[/tex] over boundary B, where B is the ball of radius 2 centered at the origin.

2. Relevant equations

Using spherical coordinates:

x=psin[tex]\Phi[/tex]cos[tex]\Theta[/tex]

y=psin[tex]\Phi[/tex]sin[tex]\Theta[/tex]

z=pcos[tex]\Phi[/tex]

Integral limits:

dp - [0,2]

d[tex]\Phi[/tex] - [0,[tex]\pi[/tex]]

d[tex]\Theta[/tex] - [0,2[tex]\pi[/tex]]

3. The attempt at a solution

I am just having trouble finding a good substitution for the integrand. When I substitute x,y, and z with the spherical substitutions, I just get a huge jumbled mess that I can't make any sense of.

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# Homework Help: Triple Integral with Spherical Coordinates

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