1. The problem statement, all variables and given/known data To integrate a function (the function itself is not important) over the region Q. Q is bounded by the sphere x²+y²+z²=2 (ρ=sqrt2) and the cylinder x²+y²=1 (ρ=cscφ). To avoid any confusion, for the coordinates (ρ,φ,θ), θ is essentially the same θ from polar coordinates in 2 dimensions while φ is the angle measured from the +z axis to ρ. 2. Relevant equations Jacobian = ρ²sinφ 3. The attempt at a solution I can see that the limits for ρ go from cscφ to sqrt2. Also θ should go from 0 to 2pi. But I'm not sure how to find the limits for φ (the book says it goes from pi/4 to 3pi/4). How is it justified?