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Exam_solutions_3_(2)

# Exam_solutions_3_(2) - MATH 141 TEST 3(8.1 8.7[Pilachowski...

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Math 141, Sections 03**, T Pilachowski, Spring 2007 March 30, 2007 MATH 141 – TEST 3 (8.1 – 8.7) [Pilachowski] SOLUTIONS 1. (15 points) Evaluate dx x x 2 ln . (Show integral-calculus work and state an answer in simplest form.) x x v dx x dv dx x du x u 1 , , 1 , ln 1 2 = = = = = x x x dx x x x x dx x x 1 ln 1 1 1 ln ln 2 = = 2. a. (15 points) Evaluate dx x x 5 3 cos sin . (Show integral-calculus work; answer in simplest form.) dx x du x u sin , cos = = ( ) ( ) C x x C u u du u u du u u dx x x x dx x x x dx x x + + = + + = = = = = 8 6 8 6 7 5 5 2 5 2 5 2 5 3 cos 8 1 cos 6 1 8 1 6 1 1 sin cos cos 1 sin cos sin cos sin b. (10 points) Evaluate dx x 2 sin . (Show integral-calculus work; answer in simplest form.) 4 2 sin 2 1 2 2 cos 2 1 2 2 cos 1 sin 2 x x dx x dx x dx x = = = 3. (20 points) Evaluate + dx x x 9 2 3 . (Show integral-calculus work; answer in simplest form.) u x u dx u x x u 2 2 2 sec 9 9 , sec 3

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