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I am having trouble setting up the region of integration for a sphere centered at (0,0,1) with a radius of 1 using spherical coordinates. I know the upper bound for rho is 2cos(phi) but I cant figure out the lower bound.

P.S. I know there is a way to change to make (0,0,1) the new origin but I know that is not what I am supposed to do for this problem so would prefer to know some other way especially since the equation I am integrating is $\sqrt(x^2+y^2+z^2)$

Andrew
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  • http://math.stackexchange.com/questions/1254777/spherical-coordinates-for-sphere-with-centre-neq-0. I think that answer will help. – Zaros Nov 29 '16 at 01:26
  • it helped some but I am still struggling to understand and picture the bounds and how they are changed by the shifted sphere. so $\theta$ would still be from 0 to 2pi? and phi from 0 to pi? – Andrew Nov 29 '16 at 01:52

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