1. The problem statement, all variables and given/known data Find the volume of the region bounded by the cylinder x^2 + y^2 =4 and the planes z=0, and x+z=3. 2. Relevant equations V = ∫∫∫dzdxdy V=∫∫∫rdrdθ 3. The attempt at a solution Alright, so I feel as though I'm missing a step somewhere along the way, but here's what I've gotten so far. So I know that I've got a cylinder centered around the z-axis, bounded by z=0 (which would be the xy-plane) and x+z=3. If I attempt a triple integral in Cartesian coordinates, beginning with the z limits of integration, I enter the region at z=0, and exit the region at z=3-x? I'm having a hard time picturing the x=3-x part since y=0, and so we aren't actually looking at the whole cylinder? Well from there, I looked at the circle cast by the cylinder on the xy-plane, x^2+y^2 = 4. I solved for y for my y limits of integration, -(4-x^2)^1/2 to + (4-x^2)^1/2. And then my x limits are simply -2 to 2. I feel like I'm not taking into account the z=3-x for my y and x limits, though I'm not sure how I would... Here's my attempt in cylindrical coordinates. Since x^2+y^2 = r^2=4, I said my r limits are from r=0 to r=2. My z limits are from z=0 to z=3-rcosθ. And my limits for θ are from 0 to 2pi. I feel like I'm missing something...Any help in the right direction would be greatly appreciated! Thanks!