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138ass2

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

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