138ass2 - MATH 138 Assignment 2 Spring 2009 Methods of...

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MATH 138 Assignment 2 Spring 2009 Methods of integration and applications: volumes and integration of rational functions by partial fractions. Submit all problems marked (*) by 12:30 p.m. on Friday, May 22. 1. ( * ) Find the volume of the solid obtained by rotating the region bounded by the given curves about the given axis. Sketch the region, the solid and the disks or washers. (a) y = 1 /x , x = 1, x = 3, y = 0, about the x -axis. (b) y = 1 / 4 x 2 , x = 2, y = 0, about the y -axis. (c) y = 1 / 4 x 2 , y = 5 - x 2 , about the x -axis. (d) y = In x , y = 1, y = 3, x = 0, about the y -axis. 2. The following integrals represent the volume of a solid. Explain how to obtain the solid by rotating a region of the xy -plane (describe the region and give the axis too!). (a) π R 5 2 y dy . (b) π R π/ 2 0 ((1 + cos x ) 2 - 1) dx . 3. Find the volume of the solid S . (a) ( * ) S is a pyramid with height h and rectangular basis with dimensions b and 2 b . (b) (
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This note was uploaded on 01/19/2010 for the course MATH 138 taught by Professor Anoymous during the Spring '07 term at Waterloo.

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138ass2 - MATH 138 Assignment 2 Spring 2009 Methods of...

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