I'm studying for my calculus exam and having difficulty with this question.
Find the volume lying between the paraboloids and .
I know to switch to polar coordinates, so and . The solution to the question says that they intersect where , which I understand is just because you're setting z=z and solving, and that r can also be subbed in to be . But then the solution says they intersect at that equation where z=z, "i.e. on the cylinder . Is this just solving for from the ?
I suppose my question is, what is the process I follow to solve this question? The solution integrates over the disc of radius 1, sets the intersection equation to zero with everything on one side, and integrates. But I don't know why.
The final answer is cubic units.
Thanks so much for your help.