Math151OldSols1

Math151OldSols1 - QUIZ ON CHAPTER 9 SOLUTIONS MATH 151...

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QUIZ ON CHAPTER 9 SOLUTIONS MATH 151 – SPRING 2003 – KUNIYUKI 100 POINTS TOTAL Evaluate the following integrals. 1) sin cos 65 xx d x Ú (10 points) The odd power involves cos x , so peel off one cos x factor. (We will let u be the “other guy,” namely sin x .) =◊ Ú sin cos cos 64 x d x We then want to rewrite cos 4 x as a power of cos 2 x and then use a Pythagorean identity to make more “ u ”s. = () =- Ú Ú sin cos cos sin sin cos 62 2 2 1 x d x x d x Let ux du x dx = = sin cos + + Ê Ë Á ˆ ¯ ˜ ++ =-+ + Ú Ú Ú uu d u u d u u d u u C x x C 2 4 68 1 0 79 1 1 1 1 1 12 2 7 2 91 1 1 7 2 9 1 11 Go back to !! sin sin sin 2) tan sec 53 d x Ú (10 points) We have an odd power of tan x , so peel off a sec tan factor. (We will let u be the “other guy,” namely sec x .) Ú tan sec sec tan 42 xxx x d x We then want to rewrite tan 4 x as a power of tan 2 x and then use a Pythagorean identity to make more “ u ”s.
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= () =- Ú Ú tan sec sec tan sec sec sec tan 2 2 2 2 2 2 1 xx x x d x x x d x Let ux du x x dx = = sec sec tan + + Ê Ë Á ˆ ¯
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Math151OldSols1 - QUIZ ON CHAPTER 9 SOLUTIONS MATH 151...

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