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) = 4x³zi + 4y³zj + 3z⁴k, S is the sphere with radius R and center the origin

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