I am having trouble with the following question:
Evaluate the triple integral over E, where E lies between the spheres rho = 2 and rho = 4, and above the cone phi = pi/3. The density function is given by xyz dV.
When I change variables I get the following as my density function:
(rho^5)*(sin^3(phi))*cos(phi)*cos(theta)*sin(theta ). Is this right? This doesn't seem like the easiest integral to work with, since after you integrate with respect to rho, you are left with a bunch of trig. Maybe there is another way to write the density function that I'm not seeing?
Any ideas would be great. Thanks.