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Unformatted text preview: not required to evaluate the integral.] 6. (14 points) Find the area of the part of the surface z = 2 x + y 2 that is directly over the triangle in the xy plane with vertices (0 , 0), (0 , 1) and (1 , 1). 7. (12 points) Find the work done by the force ±eld F = ± cos(ln( xy + 1)) xy + 1 + 2 x sin x 2 ,cos(ln( xy + 1)) xy + 1 + 3 y 2 e y 3 ² . to move an object counterclockwise around the boundary of the region in the ±rst quadrant lying between the curves y = x 2 and y = √ x . 8. (12 points) Use Stokes’s Theorem to evaluate Z Z G curl v · n dS , where v = yz i + x j + ( y + z ) k and G is the part of the paraboloid z = x 2 + y 2 below the plane z = 4, with the upward normal....
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This note was uploaded on 04/07/2008 for the course MATH 265 taught by Professor Gregorac during the Spring '08 term at Iowa State.
 Spring '08
 Gregorac
 Math, Calculus

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