Assignment 2

# Assignment 2 - -x 2 , [0 , 9]. 3. Evaluate each of the...

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Math 138 Assignment 2 Fall 2008 The following questions are to be answered neatly and completely on standard size (8.5 by 11 inch, or metric equivalent) paper. Please insure that your name and ID number are clearly indicated on each page, and that all your pages are securely fastened together, staples are preferred. This assignment is due at 9:00 a.m. on Friday, September 26, 2008 . 1. Determine the volume obtained by rotating the region deﬁned by the given curves about the speciﬁed line. Include a sketch of the region with a typical cylindrical shell, and sketch the solid. a) x = 4 y 2 - y 3 , x = 0; about the x -axis. b) x + y = 3, x = 4 - ( y - 1) 2 ; about the x -axis. c) y = x 2 , x = y 2 ; about x = - 1. 2. For each of the following functions, f : a) Find the average value of f on the interval given. b) Find c such that f ave = f ( c ). i) f ( x ) = x - 2, [2 , 6]. ii) f ( x ) = 4 x
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Unformatted text preview: -x 2 , [0 , 9]. 3. Evaluate each of the following indenite integrals: a) R ( xe-x ) dx b) R ( x 2 cos( mx )) dx b) R ( s 2 s ) ds 4. Use the reduction formula Z (ln x ) n dx = x (ln x ) n-n Z (ln x ) n-1 dx to evaluate Z e 1 (ln x ) 5 dx. 5. Evaluate each of the following indenite or denite integrals. a) R 2 cos 5 x dx b) R tan 3 (2 x ) sec 5 (2 x ) dx c) R cos( x ) cos(4 x ) dx Please note that assignments may be submitted to the drop box before the due date. Assignments will be removed from the drop box shortly after the time they are due. The drop boxes are located on the fourth oor of the Math and Computer building (MC) outside room MC 4066. Check the course outline for the box/slot for your assignment....
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## This note was uploaded on 10/21/2010 for the course MATH 138 taught by Professor Anoymous during the Fall '07 term at Waterloo.

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