Chapter62003solutions - Chapter 6 Test December 9, 2003...

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Unformatted text preview: Chapter 6 Test December 9, 2003 Name 1. Evaluate cccc 6 cccc 3 I csc 2 x cos x M dx = cccc 6 cccc 3 1 ccccccccccccccc sin 2 x cos x dx = cccc 6 cccc 3 csc x cot x dx = A csc x D cccc 6 cccc 3 = 2 cccccccccc !!! 3 2 = 2 !!! 3 6 cccccccccccccccc cccccccc 3 2. Evaluate e 2 x cos x dx u = e 2 x v = sin x du = 2 e 2 x dx dv = cos x dx = e 2 x sin x + 2 A e 2 x sin x dx E u = e 2 x v = cos x du = 2 e 2 x dx dv = sin x dx e 2 x cos x dx = e 2 x sin x + 2 A e 2 x cos x 2 e 2 x cos x dx E or I = e 2 x sin x 2 e 2 x cos x 4 I s o I = 1 cccc 5 e 2 x sin x 2 cccc 5 e 2 x cos x + C 3. Solve the intial value problem. Support your answer by overlaying your solution on a slope field for the differential equation. dy ccccccc dx = sin i k j j x cccc 2 y { z z , y H L = 1 2 2 1 1 2 3 y = sin i k j j x cccc 2 y { z z dx = 2 cos i k j j x cccc 2 y { z z + C and y H L = 2 cos i k j j ccccccc 2 y { z z + C = 1 C = 1 s o y = 2 cos i k j j x cccc 2 y { z z + 1 4. Solve the following differential equation by the technique of separation of variables :4....
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Chapter62003solutions - Chapter 6 Test December 9, 2003...

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