Use the Divergence Theorem to calculate the surface integral S F ds; that is, calculate
Question:
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)=x4i – x3z2j + 4xy2zk, S is the surface of the solid bounded by the cylinder x2 + y2 = 1 and the planes z = x + 2 and z = 0
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
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