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Unformatted text preview: ( x,y ) = y occupying the triangle with vertices (0 , 0), (1 , 1), and (1 , 1). 6. Convert the integral below from cylindrical coordinates to an equivalent integral in a) Cartesian, b) spherical coordinates. DO NOT EVALUATE. I = Z Z 1 Z 3 r r 2 sin d z d r d . 7. Let S be the solid sphere centered at the origin with radius 2, let F = (3 xz 2 + 2 yz 2 ) i + (3 x 2 z 3yz 2 ) j + (3 x 2 y 2 + z 3 ) k , and let n be the outward pointing unit normal vector on the boundary of S . Calculate RR S F n dS . 8. Consider the vector eld F ( x,y ) = h 3 xy, 2 z, 4 xz i . a) Calculate curl F and div F . b) Use Stokes Theorem to calculate R C F T d s , where C is the triangular path from (2 , , 0) to (0 , 3 , 0) to (0 , , 2) and back to (2 , , 0)....
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 Spring '08
 Hotlz
 Math, Calculus

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