Evaluate the following integrals 10 points...

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MAC 2312-01,02,03 Calculus II FINAL EXAM SOLUTION December 11, 2008 Dr. Jungmin Choi Name Instructions. 1. This test has 10 pages including this page. There are 12 problems. 2. Show all your work. You may not receive any credit from a correct answer, if there is no relevant work leading to the answer. 3. Do not separate the pages of the test. If any pages do become separated, write your name on them and point them out to your instructor when you turn in your test. 4. You are not allowed to use a calculator. 5. Please turn off all cell phones and pagers and remove all headphones. Problem Points Score 1 40 2 10 3 15 4 10 5 10 6 15 7 10 8 40 9 15 10 10 11 10 12 15 Total 200 You may need the following formulas. sin 2 θ = 1 2 (1 - cos 2 θ ) cos 2 θ = 1 2 (1 + cos 2 θ ) 1
1. Evaluate the following integrals. (10 points each) (a) x sin xdx Using integration by parts with u = x and dv = sin xdx , the answer is - x cos x + sin x + C (b) 1 0 1 4 - x 2 dx Using trig substitution of x = 2 sin θ , the answer is π/ 6 .

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