Math241_Fall08_2PM_Exam4 - Math 241 Exam 4 2PM V1 Name:...

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Unformatted text preview: Math 241 Exam 4 2PM V1 Name: December 8, 2008 Section Registered In: 55 points possible 1. Consider a metal wire in the shape of the parabola y = x 2 , 1 x 3. (a) (3pts) Find a parametrization of the wire. (b) (6pts) The density at a point ( x,y ) on the wire is given by f ( x,y ) = 3 y x g/cm. Assum- ing that the units on the x-axis are in centimeters, compute the mass of the wire. (c) (2pts) If your parametrization in C was reoriented, how could that effect the integral computed in part (b)? Briefly explain your answer. 2. (a) (5pts) Compute Z C y dx- xdy x 2 + y 2 , where C is the circle of radius 1 centered at the origin, oriented counterclockwise. (b) (3pts) State the formula at the conclusion of Greens Theorem. (c) (3pts) Would Greens Theorem have been an appropriate alternative to evaluating the line integral in part (a)? Briefly explain your answer. 3. (a) (4pts) Let S be the sphere x 2 + y 2 + z 2 = 16. Parametrize the sphere....
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This note was uploaded on 02/15/2011 for the course MATH 241 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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Math241_Fall08_2PM_Exam4 - Math 241 Exam 4 2PM V1 Name:...

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