1. Let F Be a Function for Which
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. e4/16 - 5/16 / B. e4/8 - 1/72 / C. (1/4)e4 – 1D. e4/2 - 1/18 / E. (3/2)e4 + 1/2
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. 162/5D. 324/5 / E. 81
4. What is the area of the closed region in R3 bounded by the polar curve
A. / B. / C.D. / E.
5.
A. –209/20 / B. –59/8 / C. –27/8D. –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 x2 + y2 = 16 ?
A. 0 / B. 32/3 / C. 32D. 64 / E. 128
7.
A. 1 / B. (1/4)(e4 – 1) / C. (1/4)(e – 1)D. e4 - 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 y2 = 2x and y2 = 8 – 2x. Then
A. 64/5 / B. 128/5 / C. 128/3D. 256/5 / E. 256/3
10.
A. (e – 1)/3 / B. e/3 / C. e + 1D. e - 1 / E. e
11.
A. 7/6 / B. 5/4 / C. 4/3D. 7/2 / E. 15/4
12.
A. / B. / C.D. / E.
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.
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. 1/6D. 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. 9D. 21/2 / E. 11
17.
A. (e – 1)/3 / B. e/3 / C. 1D. 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 y2 = 4 – x and y2 = 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 y2 = x + 1 ?
A. 10/3 / B. 9/2 / C. 37/6D. 20/3 / E. 17/2
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. 3/2D. 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 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?
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 = y2. Which of the following iterated integrals is equal to
A./ B.
/ C.
D.
/ E.