MATH 152 FALL SEMESTER 2009 COMMON EXAMINATION I VERSION B Name print Signature Instructor s name Section No INSTRUCTIONS 1 In Part 1 Problems 1 10 mark your responses on your ScanTron form using a No 2 pencil For your own record mark your choices on the exam as well 2 Calculators should not be used throughout the examination 3 In Part 2 Problems 11 16 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 1 Part 1 Multiple Choice 50 points Each question is worth 5 points Mark your responses on the ScanTron form and on the exam itself Z p 1 Compute the indefinite integral x3 2 x4 dx a 2 x4 3 2 C 4 b 2 x4 3 2 C 6 c 2 2 x4 3 2 C 3 d 2 x4 1 2 C 8 e 2 x4 1 2 C 2 2 Compute the indefinite integral Z ex 1 ex 10 dx a 10 1 ex 9 C b 1 ex 11 C c 1 ex 11 C 11 d ex 1 ex 11 C 11 e ex e10x C 2 3 Evaluate the definite integral Z 4 0 sec2 d 3 tan 3 a ln 2 b ln 12 c ln 4 d ln 8 4 e ln 3 4 Determine the value of the positive number b for which the average value of the function f x 2 6x on the interval 0 b is 3 a 3 b 1 3 c 10 1 3 d 2 e 1 6 5 Compute the indefinite integral Z xe 3x dx xe 3x e 3x a C 3 9 xe 2x e 2x b C 2 4 c xe 2x e 2x C d xe 3x e 3x C e x2 e 2x C 2 3 6 Compute the indefinite integral a Z 2 cos2 d sin 2 C 2 b 2 sin 2 C c sin 2 C 2 4 d sin 2 C 2 4 e sin 2 C 2 7 Calculate the area of the region enclosed by the x axis y ln x x e and x e3 a e2 b 1 1 3 e e c 1 1 2 e e d 2e3 e 3 2 8 An aquarium 2 m long 1 m wide and 1 m deep is full of water Find the work needed to pump half the water out of the aquarium The density of water is 1000 kg m3 and acceleration due to gravity g is 9 8 m s2 a 250 J b 9 8 103 J c 2 45 J d 2 45 103 J e 4 9 J 4 9 Let R denote the region enclosed by the y axis the line y 1 and the curve y x Compute the volume of the solid whose base is R and whose cross sections perpendicular to the y axis are semicircles a 2 b 10 c 20 d 24 e 40 10 Suppose that f is continuous on and that F is an antiderivative of f in Which of following is an antiderivative of the function g x f 3x 2 a F 2x 3 2 b F 3x 2 c F 2x 3 d F 3x 2 3 e insufficient information to make a determination 5 Part 2 56 points Present your solutions to the following problems 11 16 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 11 10 points Compute the following integral Z cos3 x dx x 6 12 10 points Compute the following integral Z sec3 x tan3 x dx 7 13 10 points Let R denote the region bounded by the parabola y 1 x2 and the straight line y 2x 2 Sketch R and calculate its area 8 14 10 points Let R denote the region enclosed in the first quadrant by the x axis the line x 1 and the curve y x3 Sketch R and use the method of cylindrical shells to calculate the volume of the solid obtained by rotating R about the line x 1 9 15 10 points Let T denote the triangular region with vertices at 0 0 2 1 and 4 1 Sketch T and use the method of disks to compute the volume of the solid obtained by rotating T about the y axis 10 16 6 points Let f be a function such that f is continuous in the interval 0 Given that Z f 0 1 f 1 and f x sin x dx 4 0 evaluate Z f x sin x dx 0 11 QN PTS 1 10 11 12 13 14 15 16 TOTAL 12
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