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

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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

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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