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Surface Integral (Integral Setup)

  • #1

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
 

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Answers and Replies

  • #2
BvU
Science Advisor
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2019 Award
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Hi,
for the surface integral dS would become 9sin(phi)
I hope you mean ##9 \sin\phi \;
d\theta d\phi## :rolleyes:
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 !
 

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