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Mth 277
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Question 5 cont
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Use spherical coordinates to compute the triple integral of z / (x^2 + y^2 + z^2) with respect to V over D where D is the solid bounded above by the sphere x^2 + y^2 + z^2 = 4 and below by the surface phi = pi/6.
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All I need to know, what is the function that we are integrating. The bounds are rho from 0 to 2 phi from 0 to pi/6 and theta from 0 to 2pi. I now understand this. Thanks for that thorough explanation. But what about the function, the base part that we are actually integrating? Doesn't it also have to be in terms of rho, phi, and theta? How do we convert this and what exactly do we convert? Do we take the x^2+y^2+z^2 and replace it with rho^2? And what about the z on top? Do we just replace that with rho cos(phi)?? It is all starting to come together, now I am just having issues with determining the functions. I believe I am on the right track, I just want to confirm before I submit my work again to you.
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It's as you've said. Good.
Just to be sure:
The function you are integrating is z / (x^2 + y^2 + z^2), which in spherical coordinates is r cos(phi) / rho^2 = cos(phi) / rho.
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