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Unformatted text preview: Z C Â·Â·Â· = ZZ D 1 dA. Checking the region, using y = x 2 in the equation x = y 2 gives x = x 4 , so x 4x = x ( x1)( x 2 + x + 1) = 0 , with solutions x = 0 , 1 . Solving x = y 2 for y = âˆš x gives the iterated integral Z 1 Z âˆš x x 2 1 dydx = Z 1 â€¡ [ y ] âˆš x x 2 Â· dx = Z 1 ( âˆš xx 2 ) dx = h 2 3 x 3 21 3 x 3 i 1 = 2 31 3 = 1 3 . Week 13 Homework: 16.5 Curl and Divergence Problem 16.5.5: Find Div( Â± F ) and Curl( Â± F ) when Â± F = < e x sin y, e x cos y, z > . Solution: For Â± F = < P, Q, R >, Div( Â± F ) = P x + Q y + R z , so Div( Â± F ) = e x sin ye x sin y + 1 = 1 . Using the cross product formula we have Curl( Â± F ) = < R yQ z , R xP z , Q xP y > = < , , > . Notice that if Â± F = < f x , f y , f z > is the...
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 Fall '06
 YUKICH
 Integrals, Vector Calculus, Line integral, Stokes' theorem, 2 Week, 3 Week

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