Student (Print) SectionLast, First MiddleStudent (Sign)Student IDInstructorMATH 152, Fall 2007Common Exam 1Test Form AInstructions: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 collectedafter 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 /5011 /1012 /1013 /1014 /1015 /10TOTAL1Part I: Multiple Choice (5 points each)There is no partial credit.1.Compute∫01xex2+1dxa.12eb.12(e − 1)c.12e2d.12(e2− 1)e.12(e2− e)2.Compute∫0π/2xcosxdxa.π2− 1b.1 +π2c.π2d.1 − πe.π − 13.Find the area below the parabola, y = 3x − x2, above the x-axis.a.12b.92c.272d.812e.10324.Find the average value of f(x)=e3xon the interval[0,2].a.13(e6− 1)b.13e6c.16(e6− 1)d.16e6e.(e6− 1)5.The region shown at the right is boundedabove by y = sinx and below by the x-axis.It is rotated about the x-axis.Find the volume swept out.0 1 2 30.00.51.0xya.π22b.2π2c.2πd.π2e.π46.The region in Problem 5 is rotated about the the line x = −1.Which formula gives the volume swept out?a.∫0ππ(1 + sinx)2− 1 dxb.∫0π2π(x + 1)sinxdxc.∫0ππ(x − 1)sinxdxd.∫−1π2πxsinxdxe.∫0ππ(1 + sinx)2dx37.The region bounded by the curves x = 1, y = 1 and y =4xis rotated about the x-axis.Find the volume swept out.a.π(8ln4 − 15)b.π(15 − 8ln4)c.12πd.9πe.8π8.A solid has a base which is a circle of radius 2and has cross sections perpendicular to the y-axiswhich are isosceles right triangles with a legon the base. Find the volume of the solid.a.323b.643c.1283d.163πe.323π49.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 Newtonsb.18 Newtonsc.12 Newtonsd.6 Newtonse.24 Newtons10.Find the partial fraction expansion for f(x)=5x2+ x + 12x3+ 4x.a.1x+3x − 2x2+ 4b.2x+x − 3x2+ 4c.1x+2x + 3x2+ 4d.2x+3x + 1x2+ 4e.3x+2x + 1x2+ 45Part II: Work Out (10 points each)Show all your work. Partial credit will be given.11.Computea.(5 points)∫cos3θdθb.(5 points)∫x3lnxdx612.Find the area between the cubic y=x3−x2and the line y=2x.13.A water tower is made by rotating the curve y = x4about they-axis, where x and y are in meters. If the tower is filled with water(of density ρ = 1000 kg/m3) up to height y = 25 m, how muchwork 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 ρg.714.Compute∫01x2(4 − x2)3/2dx15.Compute∫04x − 4x2+
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