1. The problem statement, all variables and given/known data Let F = <x, z, xz> evaluate ∫∫F⋅dS for the following region: x2+y2≤z≤1 and x≥0 2. Relevant equations Gauss Theorem ∫∫∫(∇⋅F)dV = ∫∫F⋅dS 3. The attempt at a solution This is the graph of the entire function: Thank you Wolfram Alpha. But my surface is just the half of this paraboloid where x is positive. So I thought if I looked down the x-axis I would get something like this: But only the right half of the circle (from -3π/2 to π/2)... The integral I set up is the following: ∫∫∫xdzdxdy (x is the dot product of ∇ and F) I converted to polar coordinates ∫∫∫r2cosθdzdrdθ Bounds: r2≤z≤1 0≤r≤1 -3π/2≤θ≤π/2 I ended up getting -(4/15)∫cosθdθ -3π/2≤θ≤π/2 (4/15)[sin(π/2)-sin(-3π/2)] = 0 Answer should be 4/15 according to the back of the book.