i need some help.
My problem is:
"Find the volume cut out of the sphere x^2 + y^2 + z^2 = 4a^2 by the cylinder x^2 + y^2 = 2ax."
I turned these equations to polar coordinates: z = 4a^2 - r^2 (this is under a root sign) and r = 2acosx (x is theta here).
The integral I set up is a double integral with limits from -pi/2 to pi/2 and the second integral from 0 to 2acosx and the integrand is (4a^2 - r^2)^0.5 r dr dx (where x is theta here).
I have a negative result (-32a^3/9), which must be wrong?! can somebody show me the steps toward the solution?