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Unformatted text preview: MAC 2312 Exam 1 Solutions June 2, 2011 Name:  {z } By writing my name, I swear by the honor code. Read all of the following information before starting the exam: • Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). • Circle or otherwise indicate your final answers. • This test has 5 problems and is worth 50 points, plus one bonus problem at the end. It is your responsibility to make sure that you have all of the pages! • Since time is limited, it is crucial that you think before you compute. • Good luck! 1. Let R be the region given below. a) Set up, but do not evaluate, an integral to find the volume obtained by rotating R about the xaxis. Solution : First, note that the xcoordinates of the graphs of y = sin x and y = 1 2 are x = π 6 and x = 5 π 6 . We will use the crosssection method. So taking crosssections perpendicular to the xaxis for x between π 6 and 5 π 6 gives a washer with inner radius 1 2 and outer radius sin...
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This note was uploaded on 10/13/2011 for the course MAC 2312 taught by Professor Bonner during the Summer '08 term at University of Florida.
 Summer '08
 Bonner
 Calculus

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