Use Stokes Theorem to evaluate C F dr. In each case C is oriented counterclockwise

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Use Stokes Theorem to evaluate ∫C F · dr. In each case C is oriented counterclockwise as viewed from above.

F(x, y, z) = xyi + 2zj + 3yk, C is the curve of intersection of the plane x + z = 5 and the cylinder x2 + y2 = 9


Data from Stokes Theorem

Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed, piecewise-smooth boundary curve C with positive orientation. Let F be a vector field whose components have continuous partial derivatives on an open region in R3 that contains S. Then

S F  dr = ff S curl F. dS

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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