MATH 152 Spring 2009 COMMON EXAM I VERSION A LAST NAME First name print INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 10 mark the correct choice on your ScanTron using a No 2 pencil For your own records also record your choices on your exam 3 In Part 2 Problems 11 15 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 4 Be sure to write your name section number and version letter of the exam on the ScanTron form THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature DO NOT WRITE BELOW Question Points Awarded Points 1 10 40 11 12 12 12 13 12 14 12 15 12 100 1 PART I Multiple Choice 1 4 pts Find the average value of f x x sin x2 from x 0 to x a 1 b 1 1 c 1 d e 0 2 4 pts Z 2 x3 ln x dx 1 15 16 3 4 ln 2 4 4 ln 2 3 4 ln 2 4 15 4 ln 2 16 a 4 ln 2 b c d e 2 3 4 pts A 50 foot rope that weighs 25 pounds hangs from the top of a tall building How much work is required to pull 10 feet of the rope to the top a 25 foot pounds b 900 foot pounds c 100 foot pounds d 225 foot pounds e 120 foot pounds 4 4 pts a b c d e Z cos2 2x dx 1 1 x sin 2x C 2 4 1 1 x sin 4x C 2 8 1 1 x sin 4x C 2 8 1 1 x sin 2x C 2 4 3 sin 2x C 3 3 5 4 pts The region bounded by y x2 and y 2x is revolved about the y axis Find the volume a b c d e 4 3 8 15 64 15 2 3 8 3 6 Find the area of the region bounded by y x2 and y 8 x2 a b c d e 32 3 64 3 22 3 44 3 128 3 4 7 4 pts Find the value of b so that the average value of f x 3x2 2x over the interval 0 b is equal to 2 a b 1 b b 2 4 c b 3 3 d b 4 e Not enough information 1 8 4 pts Find the volume of the solid obtained by revolving the region bounded by y y 0 x 1 and x 5 x about the y axis a 23 b 8 c 2 ln 5 4 d 5 2 e 5 5 9 4 pts Z 4 tan4 x sec4 x dx 0 a 2 35 5 12 12 c 35 1 d 5 2 e 35 b 10 4 pts Z 1 x sin x dx 0 1 b a 1 d c e 0 6 PART II WORK OUT 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 11 12 pts Find the volume of the solid obtained by rotating the region bounded by y x2 1 and y 2 about the line y 3 7 12 12 pts Find Z dx x2 9 x2 8 13 12 pts A tank is full of water and has the shape of a triangular trough 8 meters long 3 meters tall and 2 meters wide see figure Find the work needed to pump all the water to the top of the tank Note The weight density of water is 9800 Newton s per cubic meter 9 14 12 pts Find the volume of the solid described here The base of the solid is a triangle with vertices 0 0 1 0 and 0 2 Cross sections perpendicular to the x axis are squares Exam continues on next page 10 15 4 pts Consider the region bounded by y sin x y cos x x 0 and x i 4 pts Shade the bounded region on the axes provided below Be sure to clearly label all pertinent points ii 8 pts Find the area of this bounded region End of Exam 11
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