Need help with this problem ASAP!!!

[seanh1231]

The problem states: find the volume of the solid bounded by the cylinder x=y^2 and the planes z=0 and z=4-x. I'm supposed to solve using polar, and I've gotten the bounds for theta and z, but I'm not sure how to find the bounds for r. Can somebody please help me as soon as possible???? :confused:

[HallsofIvy]

The problem states: find the volume of the solid bounded by the cylinder x=y^2 and the planes z=0 and z=4-x. I'm supposed to solve using polar, and I've gotten the bounds for theta and z, but I'm not sure how to find the bounds for r. Can somebody please help me as soon as possible???? :confused:
You are required to use polar coordinates? That's vicious! The whole point of using different coordinate systems is to use the one best for the problem. Here that is clearly Cartesian coordinates!

Ah, well. The difficulty is that the boundary is made of two distinct parts: the parabola x=y^2 and the line x= 4. At (4, 2), tan(theta)= 4/2= 2. For theta from 0 to arctan(2), r goes from 0 out to x= 4= r cos(theta) so r goes from 0 to 4/cos(theta). For theta from arctan(2) to pi/2, r goes from 0 to y= x^2 or rsin(theta)= r^2cos^2(theta): r= sin(theta)/cos^2(theta). Because of the symmetry, I would recommend you not worry about the lower half-plane. Just integrate with theta from 0 to pi/2 and double.