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Test1_sol(2) - MAC 2312-01,02,03 Calculus II Test 1 Dr...

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MAC 2312-01,02,03 Calculus II Test 1 September 18, 2009 Dr. Jungmin Choi Name Instructions. 1. This test has 7 pages including this page. There are 6 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 15 2 15 3 20 4 10 5 30 6 10 Total 100 You may need the following formulas. sin - 1 udu = u sin - 1 u + 1 - u 2 + C, cos - 1 udu = u cos - 1 u - 1 - u 2 + C u sin - 1 udu = 2 u 2 - 1 4 sin - 1 u + u 1 - u 2 4 + C, u cos - 1 udu = 2 u 2 - 1 4 cos - 1 u - u 1 - u 2 4 + C sin 2 x = 1 2 (1 - cos 2 x ) , cos 2 x = 1 2 (1 + cos 2 x ) , sin x · cos x = 1 2 sin2 x sin A cos B = 1 2 [sin( A - B ) + sin( A + B )] , sin A sin B = 1 2 [cos( A - B ) - cos( A + B )] cos A cos B = 1 2 [cos( A - B ) + cos( A + B )] 1
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1. Evaluate the following integrals using the integration by parts.
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