Use cylindrical coordinates to find the volume of the solid in the first octant inside of the sphere x^2 + y^2 + z^2 = 4 and inside the cylinder x^2 + y^2 = 2x
Note: set up the integral only, do not evaluate.
The region they have in common is the cross sectional area of the cylinder , thus, we see that , , and the height of the solid would be defined by
In cylindrical coordinates, we can see that , , and
After a little more work, we see that the volume could be represented as
Does this make sense?
[I'm pretty sure my limits on are correct...]
--Chris