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Unformatted text preview: Math 20B, Final Exam Solutions December 7, 2006 Name: Section: This exam consists of 11 pages including this front page. Ground Rules 1. No calculator is allowed. 2. Show your work for every problem. A correct answer without any justification will receive no credit. 3. You may use two 4by6 index cards, both sides. 4. You have two hours for this exam. Score 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1 1. (a) Evaluate Z 2 1 x ln( x 2 ) dx Let u = x 2 . Then du = 2 xdx and x 1 2 u 1 4 Then Z 2 1 x ln( x 2 ) dx = Z 4 1 1 2 ln u du = 1 2 ( u ln u u ) 4 1 = 1 2 [(4 ln 4 4) ( 1)] = 2 ln 2 3 2 . (b) Find the indefinite integral Z xe x dx By integration by parts, Z xe x dx = xe x e x + C. 2 2. Compute R 2 1 1 x 1 dx . (Note: The integrand is not defined at x = 1.) Since 1 x 1 is not defined at x = 1, this is an improper integral. Thus Z 2 1 1 x 1 dx = lim t 1 + Z 2 t 1 x 1 dx = lim t 1 + 2 x 1 2 t = lim t 1 + (2 2 t 1) = 2 ....
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This note was uploaded on 04/29/2008 for the course MATH 20B taught by Professor Justin during the Fall '08 term at UCSD.
 Fall '08
 Justin
 Math

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