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Surface Integral

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cosec(x):
Hey, I want to check the answer to a question, its not in the book. Its a Surface Integral


Over the region S, the part of the sphere that lies above the cone

Using spherical substitution (phi is angle from z axis naturally :P) I get



=0

that doesn't seem right but is it?

enwiabe:
You want to have it in terms of dpd(theta), not d(phi)d(theta). Need to take into account depth.

cosec(x):
you still get a term
anyway, does that coordinate substitution work as we are working with a surface of constant radius. Thus theta and phi give the surface and the depth

enwiabe:
Nope you're not working with constant radius because the bit in between the cone and the upper hemisphere is being traced between p-values of sqrt(2)/2 and 1.

enwiabe:
Hmm I was considering the hemisphere as a whole surface btw. Because if you're tracing the OUTSIDE of that surface, then at the z-intercept p is sqrt(2)/2

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