Question

Hi there I am having some troubles trying to do my calculus homework and I really need help trying to do this problem from my homework:

Set up the problem and do not solve: The mass of the solid bounded by the surfaces 2x^2 + 2y^2= 9, z=0, z=3 with density function p(x,y)= x^2z. (Use Cylindrical Coordinates)

Please help me with this problem and shoe some steps how to set it up.

Answer 1

Cylindrical coordinates are: r, theta, and z. The differential volume element is dV = r dtheta dr rz.

The curved cylinder boundary is the circle 2r^2 = 9, r = 3/sqrt2.

The volume interval for the mass is:

3-2pi-3/sqrt2
S..S..S..r^3 z cos^2(theta)d(theta)dr dz
0--0--0

I have substituted r cos theta for x.
The S's are supposed to be integral signs. The top and bottom rows show tihe integration limits