Hello, I have to find the volume of the region enclosed by the paraboloid z=(x^2)+(y^2) and the planes z=1 and z=3 , so well i am struggling about the limits of each integral. I know that I can use cylindrical coordinates, but what about the limits in z?

Question

Hello, I have to find the volume of the region enclosed by the paraboloid z=(x^2)+(y^2) and the planes z=1 and z=3 , so well i am struggling about the limits of each integral. I know that I can use cylindrical coordinates, but what about the limits in z?
I think that there would be two triple integrals but how can I express the limits?
Please help I am really confused a lot with all of this.

Steve · Answer

cylindrical coordinates are just the regular polar coordinates, with z attached. Try ∫[0,2π]∫[1,√3]∫[r^2,3] r dz dr dθ