MidtM138SolF08

# MidtM138SolF08 - University of Waterloo Midterm Test MATH...

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Unformatted text preview: University of Waterloo Midterm Test MATH 138 Fall Term 2008 Name (Print): Solutions (Family name) (Given name) UW Student ID Number: Signature: Please indicate your section: 9:30-10:20 (P. Camir´e) Section 001 10:30-11:20 (B. Ferguson) Section 002 Course Abbreviation and Number: MATH 138 Course Title: Calculus 2 for Honours Mathematics Date of test: November 3, 2008 Time Period: Start time: 7:00 pm End Time: 9:00 pm Duration of Exam: 2.0 hours Number of Exam Pages: 8 (including this cover sheet) Exam Type: Closed Book Additional Materials Allowed: Calculator Put your answers in the spaces provided. If you need more room, use the backs of pages or page 8, and indicate where your solution is continued. Mark Distribution: Question 1 2 3 4 5 Total Value 20 10 10 10 10 60 Score MATH 138 Midterm Test Page 2 of 8 Initials: 1. Evaluate each of the following integrals:(5 marks each) a) Z π 2 cos 3 x dx = Z π 2 cos x (1- sin 2 x ) dx = Z π 2 (cos x- cos x sin 2 x ) dx = sin x- 1 3 sin 3 x π 2 = 1- 1 3 (1) 3- 0 + 0 = 2 3 b) Z √ x ln( x ) dx Use integration by parts with u = ln x , dv = √ xdx , so du = 1 x dx and v = 2 3 x 3 2 . Z √ x ln( x ) dx = 2 3 x 3 2 ln x- Z 2 3 x 1 2 dx = 2 3 x 3 2 ln x- 4 9 x 3 2 + C c) Z x 3- 5 x 2- 4 x 4- 4 x 2 dx Use a partial fraction decomposition. x 3- 5 x 2- 4 x 2 ( x- 2)( x + 2) = A x + B x 2 + C x- 2 + D x + 2 x 3- 5 x 2- 4 = A ( x 3- 4 x ) + B ( x 2- 4) + C ( x 3 + 2 x 2 ) + D ( x 3- 2 x 2 ) x 3- 5 x 2- 4 = ( A + C + D ) x 3 + ( B + 2...
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## This note was uploaded on 04/07/2010 for the course MATH 138 taught by Professor Anoymous during the Fall '07 term at Waterloo.

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MidtM138SolF08 - University of Waterloo Midterm Test MATH...

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