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Unformatted text preview: F around the closed path C equals the surface integral of curl F over S . Write S (curl F ) d S = S (curl F ) n dS = S 1,5,0 a , b , c /sqrt( a 2 + b 2 + c 2 ) dS = S ( a +5 b )/sqrt( a 2 + b 2 + c 2 ) dS , which equals ( a +5 b )/sqrt( a 2 + b 2 + c 2 ) times the area A S ; combining this with our formula A S = ( A D / c ) sqrt( a 2 + b 2 + c 2 ) we see that the original line integral equals ( a +5 b )/ c  times A D . Section 13.9: [Group Work: Group Work 1] ..?. . 1. Since div F > 0, the Divergence Theorem tells us that the net flux is positive. 2. 1 1 1 1 sqrt(1 yy ) sqrt(1 yy ) ( x 2 + y 2 ) dx dy dz = 1 1 2 1 ( r 2 ) r dr d dz = ( 1 1 dz ) ( 2 d ) ( 1 r 3 dr ) = (2)(2 )(1/4) = ....
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 Fall '11
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