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) = (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

S F. dS SSS E div F dV

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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