I just want to know how to set up the integral for this problem. Use spherical coordinates to find the volume of the solid in the first octant that lies inside a cone and a sphere.This is for practice to prepare for the real problem with functions.

Question

this is what I think how it should look like V=[0,π/2]∫() [0,π/2]∫() [ρ1,ρ2]∫()dρdφdθ Do you think i set it up right?

Answer 1

Your volume element is a weird amalgam of rectangular and cylindrical coordinates.

The volume element in spherical coordinates is
dv = r^2 sinθ dρ dφ dθ
In cylindrical coordinates,
dv = ρ dρ dφ dz

google can provide you with examples, such as

http://hyperphysics.phy-astr.gsu.edu/hbase/sphc.html