Thread: Find the centroid of a region?

Find the centroid and the moment of inertia of the the ellipse :

P= {(x,y,z):X ^2/4 + Y ^2/16 < z < 3}

with p(x,y,z)=1

use the the ellipse coordinates x = ar cos(phi) y = br sin(phi)

Who can help me with this???

It should be obvious from the symmetry that the x and y coordinates of the centroid are 0. So the question is just the z coordinate. Now, what do YOU know? What are the formulas you can use?