1. The problem statement, all variables and given/known data Given F = xyz i + (y^2 + 1) j + z^3 k Let S be the surface of the unit cube 0 ≤ x, y, z ≤ 1. Evaluate the surface integral ∫∫(∇xF).n dS using a) the divergence theorem b) using Stokes' theorem 2. Relevant equations Divergence theorem: ∫∫∫∇.FdV = ∫∫∇.ndS Stokes theorem: ∫∫(∇xF).n dS = ∫F.dR 3. The attempt at a solution The divergence theorem gives a dot product. Here we're asked for the cross product ∫∫(∇xF).n dS but the divergence of the curl will be 0. The Stokes theorem applied here is nonzero. What's wrong?