so we also have that first find the volume lying between each plane and the cylinder and then subtract the result. the volume lying between the plane and the cylinder is:
where which in polar coordinates becomes: therefore: and thus:
I've done this problem, however not in the way suggested (which I assume is much quicker and easier!)
By evaluating an appropriate double integral, ﬁnd the volume of the wedge lying between the planes and ( ) and the cylinder
(where )
I did it by switching to cylindrical polars and then doing the triple integral as I couldnt see a method using a double integral to get the answer
Using the integral
any help with doing this with a better method?