MATH 152 FALL 2010 COMMON EXAM I VERSION B 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 as 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 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 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 1 1 Compute x2 ex dx a 2xex 4ex C b x2 ex 2xex 2ex C c 2xex x2 ex C d x2 ex 2xex 2ex C 1 e x3 ex C 3 2 The base of a solid is the parabolic region between the graphs of y 1 and y x2 Cross sections perpendicular to the y axis are squares Find the volume of the solid a b c d e 1 2 2 16 9 1 6 8 15 3 A rope 20 feet long weighing 2 pounds per foot supports a 160 lb weight on the side of the building How much work in ft lbs is required to pull the weight to the top of the building a 3600 b 3200 c 1200 d 4000 e 800 2 4 Compute 4 sec4 x dx 0 a b c d e 2 3 4 3 2 2 1 3 32 5 4 2 5 5 After an appropriate substitution the integral 16 6 b c 4 d 4 e 9 6 1 following a x dx is equivalent to which of the 10 x u1 2 10u 1 2 du x u 1 2 du 1 16 9 3 10u 1 2 u1 2 du u 10u 1 du 10u 1 u du 3 6 Which integral computes the area between the curves y x 1 and x 1 y 2 3 a x 1 x 1 dx 1 2 b y 1 y 2 1 dy c x 1 x 1 dx d x 1 x 1 dx e 1 3 1 3 0 2 1 y 2 1 y 1 dy 3 7 Compute 2 1 sin 2x cos x dx 0 a 1 b 0 1 c 2 3 d 2 2 e 3 8 Compute 0 a b c d e x dx 2 x 1 5 2 4 2 2 3 3 2 1 2 2 4 2 4 4 9 Which integral gives the volume of the solid formed by rotating the region bounded by y x and y x2 about the line x 2 a 2 b x 2 x x2 dx 0 1 y 0 c 2 1 1 1 2 y y 0 d 2 e 0 2 y dy y dy 2 x x x2 dx 0 1 2 2 2 2 x 2 x dx 10 Which of the following is equivalent to a b c d e 1 4 x ln x 4 x3 ln x dx 1 3 x dx 4 x4 ln x x4 3x3 ln x 3x3 dx 1 3 1 4 x x ln x dx 4 4 x2 3x dx 3x2 ln x 3x dx 5 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 1 11 12 points Sketch the graph and find the area of the region bounded by the curve y x2 the 4 line tangent to this curve at x 8 and the x axis 6 12 8 points each Compute the following integrals a x tan 1 x dx b cos2 x tan3 x dx 7 13 12 points The conical tank shown below is 3 feet tall not including the spout has a 2 foot radius at the top is full of water density g and has a 1 foot tall spout Find the work required to pump all the water out of the spout Leave your answer in terms of and g 8 14 10 points Find the volume of the solid formed by rotating the region bounded by x 0 y 2 sin x and y sec x shaded below about the x axis 9 15 10 points Find the number s b such that the average value of f x 3x2 4x 7 on the interval 0 b is equal to 1 10 DO NOT WRITE BELOW Question Points Awarded Points 1 10 40 11 12 12 16 13 12 14 10 15 10 TOTAL 100 11
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