MATH 152, Spring 2009COMMON EXAM I - VERSION ALAST NAME, First name (print):INSTRUCTOR:SECTION NUMBER:UIN:SEAT NUMBER:DIRECTIONS:1. The use of a calculator, laptop or c omputer 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 conciselyand clearly indicate your final answer. Yo u will be graded not merely on the final answer, but also on the qualityand correctness of the work leading up to it.4. Be sure to write your name, section number and version letter of t he exam on the ScanTron form.THE AGGIE CODE OF HO NOR“An Aggie does not lie, cheat or steal, or tolerate those who do.”Signature:DO NOT WRITE BELOW!QuestionPoints Awarded Points1-10 4011 1212 1213 1214 1215 121001PART I: Multiple Choice1. (4 pts) Find the average value o f f (x) = x sin(x2) from x = 0 to x =√π.(a) 1(b) −1(c) −1√π(d)1√π(e) 02. (4 pts)Z21x3ln x dx =(a) 4 ln 2 −1516(b) 4 ln 2 −34(c) 4 ln 2(d) 4 ln 2 +34(e) 4 ln 2 +151623. (4 pts) A 50 foot rope that weighs 25 po unds hangs from the top of a tall building. How much work is required topull 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 pounds4. (4 pts)Zcos2(2x) dx =(a)12x +14sin(2x) + C(b)12x +18sin(4x) + C(c)12x −18sin(4x) + C(d)12x −14sin(2x) + C(e)sin3(2x)3+ C35. (4 pts) The region bounded by y = x2and y = 2x is revolved about the y-axis. Find the volume.(a)4π3(b)8π15(c)64π15(d)2π3(e)8π36. Find the a rea of the region bounded by y = x2and y = 8 − x2.(a)323(b)643(c)223(d)443(e)128347. (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(c) b =43(d) b =34(e) Not enough informatio n.8. (4 pts) Find the volume o f the solid obtained by revolving the region bounded by y =1x, y = 0, x = 1 and x = 5about the y-axis .(a) 23π(b) 8π(c) 2π ln 5(d)4π5(e)2π559. (4 pts)Zπ/40tan4x sec4x dx(a) −235(b)512(c)1235(d)15(e)23510. (4 pts)Z10x sin(πx) dx =(a)1π(b) π(c) −1π(d) −π(e) 06PART II WORK OUTDirections: Present your solutions in the space provided. Show all your work neatly and concisely and Box yourfinal answer. You will be graded not merely on the final answer, but also on the quality and correctness of the workleading up to it.11. (12 pts) Find the volume of the solid o bta ined by rota ting the region bounded by y = x2+ 1 and y = 2 about theline y = 3.712. (12 pts) FindZdxx2√9 − x2813. (12 pts) A tank is full of water and ha s the shape of a triangular trough 8 meters long, 3 meters tall and 2 meterswide (see figure). Find the work needed to pump all the water to the top of the tank. Note: The weight density ofwater is 9800 Newton’s per cubic meter.914. (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 page1015. (4 pts) Consider the region bounded by y = sin x, y = cos x, x = 0 and x = π.(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
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