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Unformatted text preview: solid we have the Theorem that Curl( ± F ) = ± exactly when there is f so that ± F = Grad( f ). 2 Problem 16.9.7: Use the Divergence Theorem to calculate the surface integral RR S ± F · d ± S, where ± F ( x, y, z ) = ( e x sin y ) ± i + ( e x sin y ) ± j + yz 2 ± k, and S is the surface of the box B bounded by planes x = 0 , x = 1 , y = 0 , y = 1 , z = 0 , z = 2 . Solution: The divergence div( ± F ) = = e x sin y + e x (sin y ) + 2 yz = 2 yz. So RR S ± F · d ± S = RRR B 2 yz dV = Z 1 Z 1 Z 2 2 yz dzdydx = 2 ....
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 Spring '06
 YUKICH
 Calculus, Integrals, Vector Calculus, Vector field, ex sin, Stokes' theorem

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