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. |
2.
A. e^{4}/16 - 5/16 |
B. e^{4}/8 - 1/72 |
C. (1/4)e^{4} - 1 |
D. e^{4}/2 - 1/18 |
E. (3/2)e^{4} + 1/2 |
3.Let S be the closed region in the first quadrant of the xy-plane bounded by x^{2} + y^{2} = 9, the y-axis, and the x-axis. What is
A. 27/2 |
B. 27 |
C. 162/5 |
D. 324/5 |
E. 81 |
4. What is the area of the closed region in R^{3} bounded by the polar curve
A. |
B. |
C. |
D. |
E. |
5.
A. -209/20 |
B. -59/8 |
C. -27/8 |
D. -49/20 |
E. 15/16 - 4 ln 2 |
6. What is the value of
where R is the region in the first quadrant bounded by x^{2} + y^{2} = 16 ?
A. 0 |
B. 32/3 |
C. 32 |
D. 64 |
E. 128 |
7.
A. 1 |
B. (1/4)(e^{4} - 1) |
C. (1/4)(e - 1) |
D. e^{4} - 1 |
E. e - 1 |
8. Which expression below is equal to
A. |
B. |
C. |
D. |
E. |
9. Let S be the closed region bounded by the curves y^{2} = 2x and y^{2} = 8 - 2x. Then
A. 64/5 |
B. 128/5 |
C. 128/3 |
D. 256/5 |
E. 256/3 |
10.
A. (e - 1)/3 |
B. e/3 |
C. e + 1 |
D. e - 1 |
E. e |
11.
A. 7/6 |
B. 5/4 |
C. 4/3 |
D. 7/2 |
E. 15/4 |
12.
A. |
B. |
C. |
D. |
E. |
13. What is the volume of the closed region in R^{3} bounded by the surfaces z = 0 and z = 4 - x^{2} - y^{2} ?
A. |
B. |
C. |
D. |
E. |
14. Let S be the closed region in the first octant of R^{3} 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 |
15.
A. |
B. |
C. |
D. |
E. |
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 |
17.
A. (e - 1)/3 |
B. e/3 |
C. 1 |
D. e - 1 |
E. e |
18.
A. |
B. |
C. |
D. |
E. |
19. What is the area of the closed region in the xy-plane bounded by y^{2} = 4 - x and y^{2} = 4 - 4x ?
A. |
B. |
C. |
D. |
E. |
20. What is the area of the closed region in the xy-plane bounded by y = 1 - x and y^{2} = x + 1 ?
A. 10/3 |
B. 9/2 |
C. 37/6 |
D. 20/3 |
E. 17/2 |
21. What is the area of the closed region in the first quadrant bounded by y = 0, x = y^{2}, 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 |
22. What is the area of the region bounded by the lines
A. |
B. |
C. |
D. |
E. |
23. Let S be the closed solid in R^{3} 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 |
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. |
25. Let F be the closed region in the xy-plane bounded by x + y = 2 and x = y^{2}. Which of the following iterated integrals is equal to
A. |
B. |
C. |
D. |
E. |