Math151Quiz1Sols

Math151Quiz1Sols - QUIZ 1 (CHAPTER 9) SOLUTIONS MATH 151...

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QUIZ 1 (CHAPTER 9) SOLUTIONS MATH 151 – SPRING 2004 – KUNIYUKI 105 POINTS TOTAL, BUT 100 POINTS = 100% For 1) through 8), evaluate the integrals. 1) ex d x x 2 3 sin () Ú (14 points) METHOD 1 Alternating signs Successive derivatives Successive antiderivatives + sin 3 x e x 2 (strike) - 33 cos x 1 2 2 e x + - 93 sin x 1 4 2 e x Ú d x exex d x Ie x e x I x e x xx x x II 22 2 2 3 1 2 3 3 4 3 9 4 3 1 2 3 3 4 3 9 4 13 4 1 2 3 3 4 3 sin sin cos sin sin cos sin cos "" = - - = - - = - ÚÚ Call 12 44 3 1 2 3 + = - È Î Í ˘ ˚ ˙ + = - + C x C I 4 13 1 2 3 3 4 3 sin cos 2 13 sin 3 3 13 cos 3 C
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METHOD 2 Alternating signs Successive derivatives Successive antiderivatives + e x 2 sin 3 x () (strike) - 2 2 e x - È Î Í ˘ ˚ ˙ 1 3 3 cos x + 4 2 e x - È Î Í ˘ ˚ ˙ 1 9 3 sin x Ú ex d x exex d x Ie x e x I x e xx x x II 22 2 2 3 1 3 3 2 9 3 4 9 3 1 3 3 2 9 3 4 9 13 9 1 3 3 2 9 3 sin cos sin sin cos sin cos sin "" =- + - + - + ÚÚ Call 12 44 3 1 2 3 x C x e x C I + + È Î Í ˘ ˚ ˙ + + + 9 13 1 3 3 2 9 3 cos sin 3 13 cos 3 2 13 sin 3 C (Note that this is equivalent to our previous result.) 2) cot csc 64 d x Ú (10 points) We like the fact that the csc power is even. We will let u be the “other guy,” namely cot x .
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Math151Quiz1Sols - QUIZ 1 (CHAPTER 9) SOLUTIONS MATH 151...

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