1. Let f be a function for which exists. Which of the following expressions is equal to I with the order of integration reversed?

 A. B. C. D. E. solution

2. A. e4/16 - 5/16 B. e4/8 - 1/72 C. (1/4)e4 - 1 D. e4/2 - 1/18 E. (3/2)e4 + 1/2

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3.Let S be the closed region in the first quadrant of the xy-plane bounded by x2 + y2 = 9, the y-axis, and the x-axis. What is A. 27/2 B. 27 C. 162/5 D. 324/5 E. 81

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4. What is the area of the closed region in R3 bounded by the polar curve A. B. C. D. E. solution

5. A. -209/20 B. -59/8 C. -27/8 D. -49/20 E. 15/16 - 4 ln 2

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6. What is the value of where R is the region in the first quadrant bounded by x2 + y2 = 16 ?

 A. 0 B. 32/3 C. 32 D. 64 E. 128

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7. A. 1 B. (1/4)(e4 - 1) C. (1/4)(e - 1) D. e4 - 1 E. e - 1

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8. Which expression below is equal to  A. B. C. D. E. solution

9. Let S be the closed region bounded by the curves y2 = 2x and y2 = 8 - 2x. Then A. 64/5 B. 128/5 C. 128/3 D. 256/5 E. 256/3

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10. A. (e - 1)/3 B. e/3 C. e + 1 D. e - 1 E. e

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11. A. 7/6 B. 5/4 C. 4/3 D. 7/2 E. 15/4

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12. A. B. C. D. E. solution

13. What is the volume of the closed region in R3 bounded by the surfaces z = 0 and z = 4 - x2 - y2 ?

 A. B. C. D. E. solution

14. Let S be the closed region in the first octant of R3 bounded by the coordinate planes and the plane x + y + z = 1. The mass density at any point in S is equal to the square of the distance from the point to the xy-plane. What is the mass of S ?

 A. 1/60 B. 1/20 C. 1/6 D. 6 E. 60

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15. A. B. C. D. E. solution

16. If D is the triangular region in the xy-plane with vertices (-2,1), (1,1), and (1,4), then A. 5 B. 19/3 C. 9 D. 21/2 E. 11

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17. A. (e - 1)/3 B. e/3 C. 1 D. e - 1 E. e

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18. A. B. C. D. E. solution

19. What is the area of the closed region in the xy-plane bounded by y2 = 4 - x and y2 = 4 - 4x ?

 A. B. C. D. E. solution

20. What is the area of the closed region in the xy-plane bounded by y = 1 - x and y2 = x + 1 ?

 A. 10/3 B. 9/2 C. 37/6 D. 20/3 E. 17/2

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21. What is the area of the closed region in the first quadrant bounded by y = 0, x = y2, and the line normal to this curve at (1,1)?

 A. 2/3 B. 11/12 C. 3/2 D. 13/6 E. 14/3

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22. What is the area of the region bounded by the lines A. B. C. D. E. solution

23. Let S be the closed solid in R3 bounded by the planes x = 0, y = 0, z = 0, 2x + y = 2, and x + 2y + z = 6, as shown in the figure below. What is the volume of S?

 A. 13/6 B. 3 C. 11/3 D. 13/3 E. 6

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24. Let D be a circular disk of radius 1 in the xy-plane. If the mass density at any point in D is equal to its distance to the center, what is the total mass of D?

 A. B. C. D. E. solution

25. Let F be the closed region in the xy-plane bounded by x + y = 2 and x = y2. Which of the following iterated integrals is equal to A. B. C. D. E. solution