# Surface Integral (Integral Setup)

1. Oct 21, 2016

### Ronaldo95163

1. The problem statement, all variables and given/known data
I'm just required to setup the integral for the question posted below

2. Relevant equations

3. The attempt at a solution
So solving for phi @ the intersection of the sphere and the plane z=2:

z = pcos(phi)
2 = 3cos(phi)
phi = arccos(2/3)

so my limits for phi would go from 0 to arccos(2/3)

and my limits for theta would go from 0 to 2pi

for the surface integral dS would become 9sin(phi)

The rest of the integral I can obtain from just substituting x = psin(phi)cos(theta) y = psin(phi)sin(theta) and z = pcos(phi)

What I really want to be sure of is limits of integration.

Thanks in advance guys

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2. Oct 21, 2016

### BvU

Hi,
I hope you mean $9 \sin\phi \; d\theta d\phi$
The latter for the numerator. The denominator is simply 9 -- easy !

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