Use Stokes Theorem to evaluate S curl F ds. F(x, y, z) = x 2

Question:

Use Stokes Theorem to evaluate ∫∫S curl F · ds.

F(x, y, z) = x2y3zi + sin(xyz)j + xyz k, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis


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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