Use the Divergence Theorem to calculate the surface integral ∫∫_S F · ds; that is, calculate the flux of F across S.

F(x, y, z) = e^x sin yi + e^x cos yj + yz²k, S is the surface of the box bounded by the planes x = 0, x = 1, y = 0, y = 1, z = 0, and z = 2

Data from the Divergence Theorem

Let E be a simple solid region and let S be the boundary surface of E, given with positive (outward) orientation. Let F be a vector field whose component functions have continuous partial derivatives on an open region that contains E. Then

S F. dS SSS E div F dV