1. The problem statement, all variables and given/known data Find the volume between z = x^2 + y^2 and z = 3 - x - y 2. Relevant equations None 3. The attempt at a solution I must use a double integral. Using polar coordinates I find that the volume is equal to: V = ∫∫(3 - rcosθ - rsinθ) r dr dθ - ∫∫r^2 r dr dθ I'm struggling trying to find the region of integration. I found that the projection onto the x-y plane is the circle x^2 + x + y^2 + y = 3, or (x+1/2)^2+(y+1/2)^2 = 7/2. By switching to polar coordinates I get: r^2 + rcos + rsinθ = 3 Since it's a circle, I assume that 0 ≤ θ ≤ 2∏. But what about r? I tought It went from 0 <= r <= √(7/2), but I'm not sure anymore since it's a circle centered outside the origin. What can I do?