11Breview7sol

11Breview7sol - econ 11b ucsc ams 11b Review Questions 7...

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Unformatted text preview: econ 11b ucsc ams 11b Review Questions 7 Solutions Note: The formula numbers below refer to the table of integral formulas in Appendix C. 1. a. Z 4 dx 5 x x 2 + 9 = 4 5 1 3 ln x 2 + 9- 3 x + C ! = 4 15 ln x 2 + 9- 3 x + C, (Formula #28, with a = 3). b. Z 4 2 xdx 9 + 4 x = 2 2(4 x- 18) 9 + 4 x 48 4 = 4 (- 2) 25 48- 4 (- 18) 9 48 = 11 3 , (Formula #15, with a = 9 and b = 4). c. First, using formula #39 (with n = 2), followed by formula #38, (and sim- plifying), we have Z t 2 e- . 06 t dt = t 2 e- . 06 t- . 06- 2- . 06 Z te- . 06 t dt = t 2 e- . 06 t- . 06 + 2 . 06 e- . 06 t (0 . 06) 2 (- . 06 t- 1) + C =- e- . 06 t (0 . 06) 3 ( (0 . 06) 2 t 2 + (0 . 12) t + 2 ) + C. So, Z 10 200 t 2 e- . 06 t dt =- 200 e- . 06 t (0 . 06) 3 ( (0 . 06) 2 t 2 + (0 . 12) t + 2 ) 10 =- 200 e- . 6 (0 . 06) 3 (0 . 36 + 1 . 2 + 2)-- 200 (0 . 06) 3 2 42806 . 09 . d. Z 3 dv 4 v 2 + 25 = 3 2 Z du u 2 + 25 = 3 2 ln u + u 2 + 25 + C = 3 2 ln 2 v + 4 v 2 + 25 + C, (substitute u = 2 v , so 4 v 2 = u 2 and dv = 1 2 du , then use formula #27 with...
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11Breview7sol - econ 11b ucsc ams 11b Review Questions 7...

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