1. The problem statement, all variables and given/known data Let S be the surface defined by y=10−x^2−z^2 with y≥1, oriented with rightward-pointing normal. Let F=(2xyz+5z)i+e^(x)cosyzj+(x^2)yk. Determine ∫∫∇×F·dS. 2. Relevant equations ∫∫∇×F·dS = ∫F·dS 3. The attempt at a solution I think the boundary of the surface is the circle of radius √5 in the xz plane. The parameterization of this should be equal to <√5cost,0,√5sint>. After plugging this parameterization into F and taking the dot product with dS I got ∫-25sin2tdt from 0 to 2 pi, which equals -25∏, however this is not the correct answer. I am not sure about what I am doing wrong. I would appreciate any assistance.