Use cylindrical coordinates to find the centroid of the solid.
The solid that is bounded above by the sphere x2 + y2 + z2 = 2
and below by z = x2 + y2
x = rcos(theta)
The Attempt at a Solution
I am having trouble trying to find the limits of integration for r.
I have been able to get the sphere in terms of r as z = (2-r2)1/2 and the paraboloid as z = r2
I understand that in cylindrical coordinates the region is occupied from 0<theta<2pi and r originates from origin n to the uppermost part of the sphere.
I also found that when you equate both surface z equations. you get r2 = (2-r2)1/2 . Solving for r you get radical 2 and 1. r being the furthest distance would then have the upper limit of 1. I'm not sure if this is the correct method of solving.[/B]