Converting to Spherical Coordinates....then integrating? Am I doing this right? 1. The problem statement, all variables and given/known data Consider the integral ∫∫∫(x2z + y2z + z3) dz dy dx, where the left-most integral is from -2 to 2, the second -√(4-x2) to √(4-x2) and the right-most integral is from 2-√(4-x2-y2) to 2+√(4-x2-y2) 2. Relevant equations x=ρsin(phi)cos(θ) y=ρsin(phi)sin(θ) z=ρcos(phi) x2+y2+z2=ρ2 3. The attempt at a solution So I need to convert to spherical coordinates. The first 2 integrals describe a region on the xy-plane that's a circle, centered at the origin, with a radius of 2. The distance from the origin I thought was from 0 to 4, as described the right-most integral from above. Then using the equations from above, I converted the integrand: ∫∫∫ρcos(phi)ρ2sin(phi) dρ d(phi) dθ Left-most integral: 0 to 2*pi Middle: 0 to pi/2 Right: 0 to 4 Final answer = 2144.67 (which does not feel right) I'm fairly certain I am correct for the most part, except the right most integral in the spherical-converted integral. Anyone care to check if I did everything correctly?