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Unformatted text preview: ρ = 2, below the cone φ = π/ 3 and above the plane z = 0, if the density is proportional to the distance from the origin. Use symmetry where possible. 6. (12 points) Apply Green’s Theorem to evaluate I C ( e x 2 +2 y ) dx +(sin y 3 + x 2x ) dy , where C is the triangle with vertices (0 , 0), (1 , 0) and (1 , 2), traversed in the counterclockwise direction. 7. (14 points) Evaluate ZZ R ( x + y ) sin( xy ) dA , where R is the triangle with vertices (0 , 0), ( π, π ) and ( π,π ). 8. (12 points) Compute the ﬂux of the vector ﬁeld F ( x, y, z ) = x i + ( y2 x ) j + ( xz ) k across the surface of the solid determined by x 2 + y 2 + z 2 ≤ 9, with the outward normal....
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 Spring '08
 Hotlz
 Calculus, Approximation, Critical Point, Final Exam S2010

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