Surface Integral (Integral Setup)

[Ronaldo95163]

Homework Statement

I'm just required to setup the integral for the question posted below

Homework Equations

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

 

[BvU]

Hi,

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

I hope you mean $9 \sin\phi \; d\theta d\phi$

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)

The latter for the numerator. The denominator is simply 9 -- easy !