Use Stokes' Theorem to compute the integral S curl F dS, where F(x, y, z)

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Use Stokes' Theorem to compute the integral ∫∫S curl F · dS, where F(x, y, z) = xz i + yz j+ xy k and S is the part of the sphere x2 + y2 + z2 =  4 that lies inside the cylinder x2 + y2 = 1 and above the xy-plane. (See Figure 4.)


Figure 4

xx N 0 S C x + y + z = 4 y x + y = 1


Stokes' Theorem

STOKES' THEOREM Let S be an oriented piecewise-smooth surface that is bounded by a simple, closed,

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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