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Math241_Fall08_2PM_Exam4

# Math241_Fall08_2PM_Exam4 - Math 241 Exam 4 2PM V1 December...

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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 - x dy 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 Green’s Theorem. (c) (3pts) Would Green’s 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. (b) (7pts) Evaluate ZZ S ( x 2 + y 2 + z 2 ) dS .

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Math241_Fall08_2PM_Exam4 - Math 241 Exam 4 2PM V1 December...

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