MATH 152 SPRING SEMESTER 2005 COMMON EXAMINATION I VERSION A Name print Signature Instructor s name Section No Seat No INSTRUCTIONS 1 Calculators may not be used on this exam The ScanTrons will be collected after 90 minutes 2 In Part 1 Problems 1 10 mark the correct choice on your ScanTron form using a No 2 pencil For your own record mark your choices on the exam itself as the ScanTrons will not be returned 3 In Part 2 Problems 11 15 present your solutions in the space provided Show all your work neatly and concisely and indicate your final answer clearly You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Be sure to write your name section number and version letter of the exam on the ScanTron form QN 1 10 11 12 13 14 15 TOTAL 1 PTS Part 1 Multiple Choice 50 points Read each question carefully each problem is worth 5 points 1 Find the average value of f x x sin x2 over the interval 0 1 a 2 1 b c 1 d 2 e 0 2 The force required to maintain a spring stretched 2 inches beyond its natural length is 3 pounds How much work is done in stretching the spring from its natural length to 2 feet beyond its natural length Note 1 foot 12 inches a 3 foot pounds b 18 foot pounds c 12 foot pounds d 36 foot pounds e 42 foot pounds 3 Find the area of the region bounded by y x2 1 y 0 x 0 and x 2 a 2 b 1 c 2 3 d 3 2 e 1 2 2 Z 4 Evaluate a 4 b 8 c 2 2 sin2 x cos2 x dx 0 d e 16 5 The region bounded by y ex y 0 x 0 and x 3 is revolved around the x axis Find the volume of the resulting solid a 2 e6 1 b e6 1 c 6 e 1 2 d 3 e 1 2 e 9 e 1 6 Z 6 Evaluate a 3 x ln x dx 1 9 ln 3 2 2 b 3 ln 3 2 c 9 ln 3 2 d ln 3 e ln 3 1 2 3 Z 7 sin3 x cos2 x dx a cos3 x cos5 x C 3 5 b cos5 x cos3 x C 5 3 c sin4 x cos3 x C 12 d cos3 x sin2 x C sin4 x sin6 x C 4 6 e Z 8 2 x dx 1 x 1 a 1 ln 2 b 1 ln 6 1 6 c d 1 ln 2 3 e 1 ln 2 3 9 The region bounded by y x2 and y 2x is rotated about the x axis Find the volume of the resulting solid 4 a 3 b 8 15 c 4 3 d 64 15 e 16 15 4 0 0 10 Suppose it is given that f 5 3 f 5 2 f 1 4 and f 1 1 Compute Hint Use integration by parts 75 a 2 b 11 c 12 d 9 e Not enough information to determine 5 Z 5 1 xf 00 x dx Part 2 56 points The use of a calculator is NOT permitted for this part of the exam All work must be shown in order to receive credit Refer to the front page for further instructions 11 10 points A tank is full of water Find the work required to pump all of the water to the top of the tank Note The weight density of water is g 9800 Newtons per cubic meter 1m 3m semicircle 12 10 points Find the volume of the solid S described below y2 The base of S is the ellipse x2 1 Cross sections perpendicular to the y axis are squares 4 6 13 12 points Consider the area of the region bounded by y x y 2 x and y 0 a Sketch the bounded region 3 2 1 0 1 2 3 3 2 1 0 1 2 3 b Find the volume obtained by revolving the region about the x axis 7 Z 14 12 points Evaluate dx x2 25 x2 8 Z 15 12 points Evaluate 10 dx x 1 x2 9 9
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