Problem:

A solid has the shape of the region bounded by the paraboloid $\displaystyle z= x^2 + y^2$ and the plane $\displaystyle z=4.$ The density at (x,y,z) is $\displaystyle z - (x^2 + y^2).$ Find the center of mass of this solid.

For double integral problems, the center of mass coordinates would be x= My/m and y= Mx/m (where Mx and My are moments of x and y, and m is mass), but I'm not sure how to go about what looks like to be a triple integral problem.

To find the moments of x, y, and z, would you simply take the triple integral of each variable times the density $\displaystyle z - (x^2 + y^2)$?

Appreciate any help. Thanks!