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) = (cos z + xy²)i + xe^–zj + (sin y + x²z)k, S is the surface of the solid bounded by the paraboloid z = x² + y² and the plane z = 4

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

Transcribed Image Text:

S F. dS SSS E div F dV