There is a simpler method using rotation of volumes since z = b is aligned with the axes: do you have to use one technique over another?
Plz have a look on the image I uploaded above to see my question.
I tried to solve the question, and come up with two thoughts.
I must have some wrong intuitions, I used to think method 1 and method 2 will have the same answer, but actually they don't.
Which of the integrals, dz, dr or dθ is incorrect?
and what is the correct boundary?
I've solved the problem with the technique of cylindrical coordinate(r,Θ,z).
but I don't know how to deal with this problem with spherical coordinate(ρ,Θ,φ).
could you desmonstrate how to do it in spherical coordinate? or tell me the range of φ and then let me try.