s07wk14 - and S is the surface of the box B bounded by...

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Week 14 Homework: [due Mon, Wed, and Fri] 16.7 Surface integrals (on graphs, lecture note) [due Mon] 16.8 Stokes’ Theorem [due Wed] 16.9 Divergence Theorem [due Fri] 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,
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Unformatted text preview: 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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This note was uploaded on 02/29/2008 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

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