I'm trying to find the volume of the cap of a sphere with double/triple integral. However I keep getting the wrong answer. I have a sphere with a radius of one centered at the orgine and the cap is between z=1/2 and z=1.
Here's my integral:
$4\int\limits_{0}^{\sqrt{3}/2}\int\limits_{0}^{\sqrt{1-x^2}} \int\limits_{1/2}^{\sqrt{1-x^2-y^2}} dzdydx$