MATH 152, FALL 2010COMMON EXAM I - VERSION BLAST 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. Foryour 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 workneatly and concisely and clearly indicate your final answer. You will be graded not merely onthe 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:11. Computeˆx2exdx.(a) 2xex− 4ex+ C(b) x2ex+ 2xex− 2ex+ C(c) 2xex+ x2ex+ C(d) x2ex− 2xex+ 2ex+ C(e)13x3ex+ C2. The base of a s olid is the parabolic region between the g raphs of y = 1 and y = x2. Cross-sectionsperpe ndicular to the y-axis are squares. Find the volume of the solid.(a)12(b) 2(c)169(d)16(e)8153. A rope 20 feet long weighing 2 pounds per foot supports a 160-lb weight on the side of thebuilding. 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) 80024. Computeˆπ/40sec4x dx.(a)23(b)43(c)2√2 − 13(d)325(e)4√255. After an appropriate substitution, the integ ralˆ6−1x√10 + xdx is equivalent to which of thefollowing?(a)ˆ169u1/2− 10u−1/2du(b)ˆ6−1x u−1/2du(c)ˆ16910u−1/2− u1/2du(d)ˆ43u − 10u−1du(e)ˆ4310u−1− udu6. Which integral computes the area between the curves y = x − 1 and x + 1 = y2?(a)ˆ3−1(x + 1) − (x − 1)dx(b)ˆ2−1(y + 1) − (y2− 1)dy(c)ˆ3−1√x + 1 − (x − 1)dx(d)ˆ30(x − 1) −√x + 1dx(e)ˆ2−1(y2− 1) − (y + 1)dy37. Computeˆπ/20sin(2x) cos(x) dx(a) 1(b) 0(c)12(d)32(e)238. Computeˆ10x√x2+ 1dx(a)√5 −√2(b)4√23−23(c)√2 − 1(d)√22(e) 4√2 − 449. Which integral gives the volume of the so lid formed by ro tating the region bounded byy = x and y = x2about the line x = 2?(a) 2πˆ10(x − 2)(x − x2) dx(b) πˆ10(y −√y)2dy(c) 2πˆ10(2 − y)(y −√y) dy(d) 2πˆ10(2 − x)(x − x2) dx(e) πˆ10(2 − x)2− (2 − x2)2dx10. Which of the following is equivalent toˆx3ln x dx?(a)14x4ln x −ˆ14x3dx(b) x4ln x + x4−ˆ(3x3ln x + 3x3) dx(c)14x3−ˆ14x4ln x dx(d) x2−ˆ3x dx(e) 3x2ln x −ˆ3x dx5PART II WORK OUTDirections: Present your solutions in the space provided. Show all your work neatly andconcisely and Box your final answer. You will be graded not merely on the final answer, but alsoon the quality and c orrectness of the work leading up to it.11. (12 points) Sketch the graph and find the area of the region bounded by the curve y =14x2, theline tangent to this curve at x = 8, and the x-axis.612. (8 points ea ch) Compute the following integrals:(a)ˆx tan−1x dx(b)ˆcos2x tan3x dx713. (12 points) The conical tank shown below is 3 feet tall (not including the spout), has a 2 footradius at the top, is full of water (density = ρg), and has a 1 foot tall spout. Find the workrequired to pump a ll the water out of the spout. (Leave your answer in terms of ρ and g.)814. (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.915. (10 points) Find the number(s) b such that the average value of f (x) = 3x2− 4x − 7 on theinterval [0, b ] is equal to 1.10DO NOT WRITE BELOW!QuestionPoints Awarded Points1-10 4011 1212 1613 1214 1015 10TOTAL
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