Verify that the Divergence Theorem is true for the vector field F on the region E.

F(x, y, z) = x² i + xy j + zk, E is the solid bounded by the paraboloid z = 4 – x² – y² and the xy-plane

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