How can I compute the volume of $x^2 + y^2 + z^2 = 4$ when it is cut with $x^2 + y^2 = 2y$?
The first one is a sphere and the second one is a cylinder. The general formula is
I've drawn a picture but I still cannot get the bounds correct. Can someone help me?
EDIT: You can write $2y + z^2 = 4$, and plugging in $z = 0$, I believe a maximum occurs at $y = 2$