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

F(x, y, z) = xyi + yz j + zx k, E is the solid cylinder x² + y² ≤ 1, 0 ≤ z ≤ 1

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