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

solution

 

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

solution

 

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

solution

 

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

solution

 

7.

 

A. 1

B. (1/4)(e4 - 1)

C. (1/4)(e - 1)

D. e4 - 1

E. e - 1

solution

 

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

solution

 

10.

A. (e - 1)/3

B. e/3

C. e + 1

D. e - 1

E. e

solution

 

11.

A. 7/6

B. 5/4

C. 4/3

D. 7/2

E. 15/4

solution

 

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

solution

 

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

solution

 

17.

A. (e - 1)/3

B. e/3

C. 1

D. e - 1

E. e

solution

 

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

solution

 

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

solution

 

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

solution

 

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