Chapter62003solutions

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

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Unformatted text preview: Chapter 6 Test December 9, 2003 Name 1. Evaluate โ€ก ฯ€ cccc 6 ฯ€ cccc 3 I โˆ’ csc 2 x cos x M dx = โ€ก ฯ€ cccc 6 ฯ€ cccc 3 โˆ’ 1 ccccccccccccccc sin 2 x cos x dx = โ€ก ฯ€ cccc 6 ฯ€ cccc 3 โˆ’ csc x cot x dx = A csc x D ฯ€ cccc 6 ฯ€ cccc 3 = 2 cccccccccc รจ!!! 3 โˆ’ 2 = 2 รจ!!! 3 โˆ’ 6 cccccccccccccccc cccccccc 3 2. Evaluate โ€ก e โˆ’ 2 x cos x dx u = e โˆ’ 2 x v = sin x du = โˆ’ 2 e โˆ’ 2 x dx dv = cos x dx = e โˆ’ 2 x sin x + 2 A โ€ก e โˆ’ 2 x sin x dx E u = e โˆ’ 2 x v = โˆ’ cos x du = โˆ’ 2 e โˆ’ 2 x dx dv = sin x dx โ€ก e โˆ’ 2 x cos x dx = e โˆ’ 2 x sin x + 2 A โˆ’ e โˆ’ 2 x cos x โˆ’ 2 โ€ก e โˆ’ 2 x cos x dx E or I = e โˆ’ 2 x sin x โˆ’ 2 e โˆ’ 2 x cos x โˆ’ 4 I s o I = 1 cccc 5 e โˆ’ 2 x sin x โˆ’ 2 cccc 5 e โˆ’ 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 โˆ’ฯ€ L = 1 โˆ’ 2 ฯ€ โˆ’ฯ€ ฯ€ 2 ฯ€ โˆ’ 1 1 2 3 y = โ€ก sin i k j j x cccc 2 y { z z dx = โˆ’ 2 cos i k j j x cccc 2 y { z z + C and y H โˆ’ฯ€ L = โˆ’ 2 cos i k j j โˆ’ฯ€ ccccccc 2 y { z z + C = 1 โ†’ C = 1 s o y = โˆ’ 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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This note was uploaded on 08/29/2010 for the course MATH 44323 taught by Professor Anderson during the Spring '09 term at Berkeley.

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

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