Let B be the part of solid cylinder {(x, y, z) : $x^2 + y^2 ≤ 1$} that is:
• below the hemisphere $x^2 + y^2 + z^2 = 4, z ≥ 0$;
• above the plane x + z = −2.
Compute the volume of B
I really need help setting up a double integral for this problem. I have only learnt Fubini's theorem, setting up integrals over general and rectangle regions, and changing variables to polar with the use of the Jacobian.
This is one of the practice problems assigned to practice for my test in 2 days. All I know is that I have to set this up as a double integral in terms of x and y then I will have to change it into polar coordinates. Any help will be greatly appreciated.