Math 132 Exam 1 Spring 2016 Name ID Number Section Number Section Instructor Day Time MWF 10 10 MWF 9 05 Nikolaou MWF 11 15 Nikolaou MWF 12 20 Zhao Zhao Wen Wen Yaping Lowell MW 2 30 MW 4 00 TuThu 8 30 TuThu 10 00 1 2 3 4 5 6 7 8 Section Instructor Day Time 9 10 11 12 13 15 16 Sunukjian TuThu 11 30 Benincasa TuThu 4 00 MWF 11 15 MWF 12 20 MWF 1 25 TuThu 11 30 TuThu 1 00 Farelli Bates Hart Le Johnson No calculator papers phones smart watches 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 Question MC Total 6 7 8 9 10 Total out of 100 Grade cid 107 cid 107 cid 107 cid 107 cid 107 cid 107 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 can be represented with this substitution eu2 du cid 90 I cid 90 cid 90 etan2 x sec2 x dx II ecos2 x dx cid 90 III e x 1 2 dx cid 90 IV 2 ex2 dx A III B I and III C III and IV D I II III and IV 2 5 points Which of the following integrals calculates the area enclosed by the two functions in the graph below from 0 x cid 90 2 1 cid 90 0 cid 90 3 0 cid 90 3 0 A f 1 y g 1 y dy B f x g x dx C g x f x dx f x g x dx D f x g x dx g x f x dx cid 90 3 cid 90 3 2 3 5 points Which of the following is equivalent to cid 90 x2 25 x dx cid 90 cid 90 cid 90 cid 90 A 5 tan2 d B 25 sec2 d C sin2 d D 5 sin d 4 5 points Find the derivative of the following function f x t g t dt cid 90 x2 ln 3 A x2g x2 ln 3 g ln 3 C 2x3g x2 1 3 ln 3 g ln 3 B 2x3g x2 D g x2 x 2 5 5 points Which of the following integrals would be solved using a u substitution cid 90 A sin e d cid 90 B 3 x2 7 dx cid 90 cid 32 C cid 33 x3 7x2 x x cid 90 dx D sin2 x cos3 x dx Please ll in your letter answer for questions 1 5 below 1 2 3 4 5 3 Free Response Portion Show all work for each of the following ques tions Partial credit may be awarded for questions 6 10 6 The velocity function of a particle moving along a line is given by v t 2t t2 interval 0 t 4 a 5 points Find the total displacement of the particle during the b 10 points Find the total distance traveled by the particle during the interval 0 t 4 4 7 Let R be the region enclosed by the curves y x and y 1 2x a 5 points Sketch the region R Find and label the intersection points b 5 points Find the area enclosed by the two functions c 10 points Find the volume of the solid obtained by rotating R around the y axis 5 8 Evaluate the integrals a 5 points 7x cos 3x dx cid 90 b 10 points cid 90 x2 9 x4 dx 6 9 Evaluate the integrals a 5 points cid 90 2 1 e1 x x2 dx b 5 points tan 1 x dx cid 90 7 10 Evaluate the integrals a 5 points sin5 cos6 d cid 90 b 10 points cos sin sin d cid 90 2 0 8 This page is left blank for additional work 9