Student (Print) Section Last, First Middle Student (Sign) Student ID Instructor MATH 152, Fall 2007 Common Exam 1 Test Form A Instructions: You may not use notes, books, calculator or computer. Part I is multiple choice. There is no partial credit. Mark the Scantron with a #2 pencil. For your own records, also circle your choices in this exam. Scantrons will be collected after 90 minutes and may not be returned. Part II is work out. Show all your work. Partial credit will be given. THE AGGIE CODE OF HONOR: An Aggie does not lie, cheat or steal, or tolerate those who do. For Dept use Only: 1-10 /50 11 /10 12 /10 13 /10 14 /10 15 /10 TOTAL 1 Part I: Multiple Choice (5 points each) There is no partial credit. 1. Compute ?01 xe x2+1 dx a. 12 e b. 12 (e ? 1) c. 12 e2 d. 12 (e2 ? 1) e. 12 (e2 ? e) 2. Compute ?0u03c0/2 x cosx dx a. u03c02 ? 1 b. 1 + u03c02 c. u03c02 d. 1 ? u03c0 e. u03c0 ? 1 3. Find the area below the parabola, y = 3x ? x2, above the x-axis. a. 12 b. 92 c. 272 d. 812 e. 103 2 4. Find the average value of f(x) = e3x on the interval [0, 2]. a. 13 (e6 ? 1) b. 13 e6 c. 16 (e6 ? 1) d. 16 e6 e. (e6 ? 1) 5. The region shown at the right is bounded above by y = sin x and below by the x-axis. It is rotated about the x-axis. Find the volume swept out. 0 1 2 30.0 0.5 1.0 x y a. u03c022 b. 2u03c02 c. 2u03c0 d. u03c02 e. u03c04 6. The region in Problem 5 is rotated about the the line x = ?1. Which formula gives the volume swept out? a. ?0u03c0 u03c0 (1 + sin x)2 ? 1 dx b. ?0u03c0 2u03c0(x + 1) sin x dx c. ?0u03c0 u03c0(x ? 1) sin x dx d. ??1u03c0 2u03c0x sin x dx e. ?0u03c0 u03c0(1 + sin x)2 dx 3 7. The region bounded by the curves x = 1, y = 1 and y = 4x is rotated about the x-axis. Find the volume swept out. a. u03c0(8 ln 4 ? 15) b. u03c0(15 ? 8 ln 4) c. 12u03c0 d. 9u03c0 e. 8u03c0 8. A solid has a base which is a circle of radius 2 and has cross sections perpendicular to the y-axis which are isosceles right triangles with a leg on the base. Find the volume of the solid. a. 323 b. 643 c. 1283 d. 163 u03c0 e. 323 u03c0 4 9. A certain spring is at rest when its mass is at x = 0. It requires 24 Joules of work to stretch it from x = 0 to x = 4 meters. What is the force required to maintain the mass at 4 meters? a. 48 Newtons b. 18 Newtons c. 12 Newtons d. 6 Newtons e. 24 Newtons 10. Find the partial fraction expansion for f(x) = 5x2 + x + 12x3 + 4x . a. 1x + 3x ? 2x2 + 4 b. 2x + x ? 3x2 + 4 c. 1x + 2x + 3x2 + 4 d. 2x + 3x + 1x2 + 4 e. 3x + 2x + 1x2 + 4 5 Part II: Work Out (10 points each) Show all your work. Partial credit will be given. 11. Compute a. (5 points) ? cos3u03b8du03b8 b. (5 points) ? x3 ln x dx 6 12. Find the area between the cubic y = x3 ? x2 and the line y = 2x. 13. A water tower is made by rotating the curve y = x4 about the y-axis, where x and y are in meters. If the tower is filled with water (of density u03c1 = 1000 kg/m3) up to height y = 25 m, how much work is done to pump all the water out a faucet at height 30 m? Assume the acceleration of gravity is g = 9. 8 m/sec2. You may give your answer as a multiple of u03c1g. 7 14. Compute ?01 x2(4 ? x2 )3/2 dx 15. Compute ?04 x ? 4x2 + 16 dx 8 Phil C:\Phil\Teaching\Current\151152
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