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Unformatted text preview: (b) (6 points) an iterated integral in spherical coordinates. 6. Let F ( x, y ) = ( ye xy + y ) i + ( xe xy + x ) j . (a) (7 points) Determine whether F is conservative. If so, ﬁnd f so that F = ∇ f . If not, state that F is not conservative. (b) (7 points) Let C be the perimeter of the triangle with vertices (1 , 2), (3 , 7), (2 ,1), oriented counterclockwise. Evaluate H C F · d r . 7. (12 points) Evaluate I C ln(1+ y ) dx + ± 3 + 1 1 + y ² x dy where C is the boundary of the triangle with vertices (0 , 0), (4 , 0) and (0 , 4), oriented counterclockwise. 8. (12 points) Evaluate RR ∂Q F · n dS . The vector ﬁeld F = ( yx ) i + ( zy ) j + ( yx ) k . The solid Q is the cube bounded by the planes x = ± 1, y = ± 1 and z = ± 1....
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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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