Unformatted text preview: Stony Brook STATE UNIVERSITY OF NEW YORK MAT 126 Final Exam – Fall 2013
Problem 1 Score 2 3 4 5 6 7 8 9 10 11 13 14 15 Total Percent Last Name: _____________________ First Name:_________________ Recitation #: _______ (See below) LEC 01 82782 TuTh 10:00am‐11:20am R01 82784 F 10:00am‐10:53am R02 82785 M 10:00am‐10:53am R03 82786 Tu 1:00pm‐ 1:53pm R04 82787 Th 4:00pm‐ 4:53pm R05 82788 W 5:30pm‐ 6:23pm LEC 02 82783 MWF 10:00am‐10:53am Engineering 143 R06 82789 M 12:00pm‐12:53pm S B Union 236 R07 82790 Th 10:00am‐10:53am Physics P112 Xuntao Hu R08 82791 Tu 8:30am‐ 9:23am Physics P116 Anant Atyam R10 88986 W 11:00am‐11:53am Physics P112 Cameron Crowe LEC 03 88808 TuTh 5:30pm‐ 6:50pm Engineering 145 R13 88809 M 4:00pm‐ 4:53pm S B Union 231 Xuan Chen R14 88810 Th 2:30pm‐ 3:23pm S B Union 231 Yu Zeng R16 88811 Th 7:00pm‐ 7:53pm Frey Hall 205 Simons Centr 103 Robert Andersen Mathematics P131 Maryam Pouryahya Library E4315 Ying Chi Mathematics P131 S B Union 237 Xuan Chen Zili Zhang Library E4310 Ying Chi Raluca Tanase Jaroslaw Jaracz Robert Andersen Mariangela Ferraro Directions: Answer all questions in the space provided. You may use the blank backs of pages for scrap. No other paper is permitted. Show ALL relevant work. Calculators are not to be used. Circle your final answers. Show all work in the space provided. Be sure that you don’t have answers to any question in more than one place. Answers without the required work will receive no credit. Simplify your answers. Each numbered question is worth 10 points. Note that the total number of points is 150. MAT 126 Final Exam Page 1 of 9 Reference Formulas: You may not need all of these. 1 sec 1 tan Trapezoidal Rule: 1
2 2 Average value = ∆ 2 2 1
2 2 2 … 2 1. For the function 2x do the following: a) Sketch the graph for x = 0 to x = 4 on the axes at the right. b) Approximate the area under the curve from x = 0 to x = 4 using a Riemann Sum using 4 sub‐intervals and the right endpoint of each sub‐
interval for as the sample points. Show the approximating rectangles on your graph. c) Approximate the area under the curve from x = 0 to x = 4 using the Trapezoidal Rule with n = 4. d) Compute the exact area under the curve by setting up an integral and evaluating it. MAT 126 Final Exam Page 2 of 9 sin 2. Evaluate the integral: . 3. The graph of a) 4 b) 7 is given at the right. Each square is 1 unit by 1 unit. If find the following: c) For what value of x does g have a maximum value? 4. Evaluate the integral √ sin 5. Evaluate the integral √ dx. MAT 126 Final Exam Page 3 of 9 6. Find the average value of the function f x over the interval [1, e]. 7. Calculate the length of the curve 2 over the interval 0, . 8. Find the volume of the solid of the obtained by revolving the region under the curve √sin from x = 0 to x = about the x‐axis using the Disk method. See the graph of √sin at the right. MAT 126 Final Exam Page 4 of 9 9. Let R be the region between and √ . a) Find the points of intersection of the two graphs. b) Sketch the region R on the axes provided. Pick appropriate scales for x and y. c) Use cylindrical shells to find the volume of the solid generated when the region R is revolved about the y‐
axis. 10. Evaluate the integral: MAT 126 Final Exam Page 5 of 9 11. Do either I or II NOT both. If you do both only I will be graded. I Calculate the hydrostatic force on one side of a plate in the shape of a right triangle of height 3 m and base of 2 m submerged in water vertically, with its upper vertex at the surface of the water. See the figure. The density of water is 1000 kg/m and g 9.8 m/s . Show the units of your final answer. II A rectangular tank 5 m long, 2 m wide, and 1 m deep is full of water. Find the work needed to pump the water out of the tank through a small hole at the top. (Use 9.8 m/s for g and the fact that the density of water is 1000 / ). MAT 126 Final Exam Page 6 of 9 12. Find f x if f(x) = √ sin t t dt. 13. Find the area bounded by the graphs of and 2. Sketch the graphs on your own axes. MAT 126 Final Exam Page 7 of 9 14. Evaluate the improper integral: . MAT 126 Final Exam Page 8 of 9 15. Evaluate the integral: dx using the substitution x 5 tanθ. Leave your final answer in terms of x. MAT 126 Final Exam Page 9 of 9 ...
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