Math 132 Exam 1 Spring 2015 Name ID Number Section Number Section Instructor Day Time MWF 10 10 MWF 9 05 MWF 11 15 MWF 12 20 MW 2 30 MW 4 00 Farelli Farelli Clark Clark Brown Brown Duanmu TuThu 8 30 TuThu 10 00 1 2 3 4 5 6 7 8 Oloo Section Instructor Day Time Benincasa TuThu 1 00 Benincasa TuThu 2 30 Buskin MWF 10 10 Yaping MWF 12 20 MWF 1 25 Yaping Buckman TuThu 11 30 TuThu 1 00 TuThu 2 30 9 10 11 12 13 15 16 17 Wen Wen No calculator papers or notes may be used Please don t just give an answer Clearly explain how you get it pro viding appropriate mathematical details This is a 2 hour exam Grade Question MC Total 6 7 8 9 10 Total out of 100 1 Mutiple Choice Section Choose the one option that best answers the question There is no partial credit for questions 1 5 1 5 points Which of the following integrals calculates the area of the shaded region A g x f x dx C g x f x dx B f y g y dy D g x f x dx cid 90 4 2 cid 90 4 3 2 5 points Which of the following integrals represent the volume of the x y 0 x 1 solid obtained by rotating the area enclosed by y 1 x 3 around the line y 1 A cid 90 3 1 cid 19 cid 18 1 x2 1 dx B cid 90 1 1 3 cid 18 1 y2 2 y cid 19 1 dy C cid 90 1 1 3 cid 19 cid 18 1 y2 2 y dy D cid 90 3 1 cid 19 cid 18 1 x2 2 x dx cid 90 3 1 cid 90 4 3 2 3 5 points Let h x g t dt Given the following information cid 90 x3 2x 5 about g x and g cid 48 x nd h cid 48 2 x 4 0 g x 5 7 g cid 48 x 6 3 10 2 1 A 70 B 7 C 3 D 21 4 5 points Evaluate the following derivative cid 90 ln 2 d dx 0 ex2 dx A e ln 2 2 e0 B e ln 2 2 C 0 D ln 2 5 5 points The population of a town in 1990 is 14 503 people The rate that the population is changing measured in people per year is rep resented by R t where t represents years after 1990 Which of the following integrals represents the total change in population from 1990 to 2007 A 14 503 R t dt C R t dt B 14 503 R t dt D R t dt cid 90 17 0 cid 90 2007 1990 Please ll in your letter answer for questions 1 5 below 1 2 3 4 5 cid 90 2007 1990 cid 90 17 0 3 Free Response Portion Show all work for each of the following ques tions Partial credit may be awarded for questions 6 10 6 Consider the region R enclosed by curves y x2 and y x a 5 points Sketch the region R Find and label the intersection points b 5 points Find the area of the region in part a 1 3 c 10 points Find the volume of the solid obtained by rotating R around the x axis 3 10 4 7 Evaluate the following integral cid 90 a 5 points t5 1 t3 49 dt cid 18 1 51 1 3 1 t3 51 1 t3 50 C cid 19 1 50 b 5 points cid 90 sin x tan x cos2 x dx 1 cos x 1 2 cos2 x C 5 8 Evaluate the following integrals a 5 points x5 2 ln x dx cid 90 2 1 2 7 2 7 2 ln 2 2 7 2 4 49 4 49 b 10 points cid 90 1 16 4x2 dx cid 34 1 2 ln 4 x2 2 cid 35 x 2 C 6 9 Evaluate the following integrals a 5 points sin2 cos3 d cid 90 3 0 cid 32 cid 33 3 cid 32 cid 33 5 3 2 1 5 3 2 1 3 b 5 points cid 90 sin ln x 3x dx cos ln x C 1 3 7 10 Evaluate the following integrals a 10 points x2 cos 2x dx cid 90 x 2 x2 2 sin 2x cos 2x sin 2x C 1 4 b 10 points cid 90 1 2x 1 x2 dx tan 1 x ln 1 x2 C 8 This page is intentionally left blank for additional work 9