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Using spherical coordinates, I have the limits 0<theta<2pi, 0<phi<pi/4, but I am not sure about rho. What would be the lower limit of rho? (I think the upper limit is 3)
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That's correct. Since you are in the cone, every straight line leaving the origin stays in the cone, and intersects the sphere. This means that the lower limit for ρ has to be 0.
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