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MATH 152 Fall 2022 COMMON EXAM I VERSION B FIRST NAME print LAST NAME print UIN INSTRUCTOR SECTION NUMBER 1 The use of a calculator laptop or computer is prohibited 2 TURN OFF cell phones and put them away If a cell phone is seen during the exam your exam will be collected and you will receive a zero 3 In Part 1 mark the correct choice on your ScanTron using a No 2 pencil The scantrons will not be returned therefore for your own records also record your choices on your exam 4 In Part 2 present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it THE AGGIE CODE OF HONOR 5 Be sure to fill in your name UIN section number and version letter of the exam on the ScanTron form DIRECTIONS An Aggie does not lie cheat or steal or tolerate those who do Signature 1 This page intentionally left blank 2 6 6 2x and y 2x on the interval from PART I Multiple Choice 4 points each 1 Which of the following represents the area bounded by the curves y x2 x 1 to x 6 4x x2 dx a 044x x2 dx b 044x x2 dx c d x2 4x dx e 164x x2 dx 2 The region bounded by the curves y x2 and y 1 is rotated about the line y 1 Find the volume of the resulting solid 16 x2 4x dx 464x x2 dx 14 4 1 a b c d 158 54 312 58 15 e 3 Compute cos3 2x dx sin 2x 1 sin3 2x C 3 1 sin 2x 1 sin3 2x C c 1 sin 2x 1 cos3 2x C 2 6 6 2 1 sin3 2x C d sin 2 x 3 b a 3 e None of these 4 4 8 3 6 x3 3 2 3 2 4 Compute 2 x4dx a 3 2 x4 C b 1 2 x4 C c 8 2 x4 3 2 C d None of these 2 x4 3 2 C e 1 5 Find the area bounded by y ex y e x x 0 and x 1 1 a e e1 b e 2 e1 c 1 e1 d e e 2 1 e 1 2 e 6 Compute tan3 x sec3 x dx 1 sec5 x 1 sec3 x C 1 tan5 x 1 tan3 x C 1 tan5 x 1 tan3 x C 5 3 1 sec5 x 1 sec3 x C 5 3 5 3 5 3 e sec4 x sec2 x C a b c d 5 0 3 6 3 2 8 0 2 e b d 0 2 0 2 y2 3 dy 7 Consider the region bounded by the curves y x3 y 8 and the y axis Which of the following represents the volume of this region being rotated about the x axis a 64 x dx c None of these 8 x dx 8 x dx 8 Suppose the work required to stretch a spring from its natural length to 4 m beyond its natural length is 16J How much force is needed to hold the spring stretched 6 m beyond its natural length a 12 N b 24 N c 72 N d 36 N e 18 N 9 Compute 01 a 601 b 301 c 301 d 151 e 60 x3 x2 1 4 dx 1 6 2 0 2 2 2 2 2 6 6 c 0 6 0 6 b 0 6 10 Which of the following represents the volume of the region bounded by the curves y 6x x2 and the x axis being rotated about x 1 a 0 2 x 1 6x x2 dx 6x x 1 dx 2 x 6x x dx 2 1 x 6x x dx d 2 x 1 6x x dx e x3 sin x dx 11 Compute a C x3 cos x 3x2 sin x 6x cos x 6 sin x b C x3 cos x 3x2 sin x 6x cos x 6 sin x c C x3 cos x 3x2 cos x 6x sin x 6 cos x 1 d C x44 sin x x26 1 3 1 1 cos x x sin x 6 3 x e C x3 cos x 3x2 sin x 6x cos x 6 sin x 12 Compute cos4 x sin5 x dx a None of these 1 sin10 x C b 1 sin6 x 6 10 1 cos5 x 2 cos7 x 1 cos9 x C c 1 cos5 x 1 cos9 x C d 1 sin8 x 1sin10 x C e 1 sin6 x 9 5 7 5 9 4 6 10 7 0 4 sec4 x dx 13 Compute2 3325434 25 a b c d e 2 2 1 3 14 A cable 20 feet long and weighing 6 pounds per foot is hanging off the side of a 30 foot tall building At the bottom of the cable is a bucket of rocks weighing 100 pounds How much work is required to pull 10 feet of the cable to the top of the building a 1900 ft lbs b 300 ft lbs c 900 ft lbs d 1300 ft lbs e 3200 ft lbs 15 Compute x2 ln x dx 1 a 2 9 9 b 1 e c 2 e3 1 9 9 e3 1 1 d e2 9 9 e None of these e3 e 1 8 Directions Present your solutions in the space provided Show all your work neatly and concisely and Box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 16 6 points Compute cos2 x sin2 x dx PART II WORK OUT 9 17 8 points Find the volume of the solid whose base is the ellipse x2 9y2 9 and whose cross sections perpendicular to the y axis are squares Evaluate your integral 10 18 Consider the region bounded by the curves y 5x x2 and y 5 x a 8 points Set up an integral to find the volume of the solid formed by rotating this region about the line y 3 Do not evaluate your integral b 8 points Set up an integral to find the volume of the solid formed by rotating this region about the line x 8 Do not evaluate your integral 11 19 10 points A tank filled with water is in the shape of a trough with isosceles triangles at its ends The trough is 30 meters long has a height of 9 meters and the width of the trough across the top is 6 meters The trough has a spout with height 1 meter The weight density of water is g 9800N m3 Set up an integral that will compute the work required to pump all the water out of the spout Do not evaluate Clearly …

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