Deck 14: Section 1: Multiple Integration

Question 1

Sketch the region R and evaluate the iterated integral.

A)
B)
C)
D)
E)

Answer 1

Question 2

Use an iterated integral to find the area of the region bounded by .

A)
B)
C)
D)
E) The integral is improper and does not converge.

Answer 2

Question 3

Evaluate the following integral.

A)
B)
C)
D)
E)

Answer 3

Question 4

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Question 5

Evaluate the following iterated integral.

A)
B)
C)
D)
E)

Question 6

Evaluate the improper iterated integral .

A)
B)
C)
D)
E)

Question 7

Use an iterated integral to find the area of the region shown in the figure below.

A)
B)
C)
D)
E)

Question 8

Evaluate the iterated integral by switching the order of integration. Round your answer to three decimal places.

A) 0.538
B) 0.558
C) 30.538
D) 1.538
E) 4.538

Question 9

The area of a region R is given by the iterated integral . Switch the order of integration and show that both orders yield the same area. What is this area?

A)
B)
C)
D)
E)

Question 10

Evaluate the following improper integral.

A)
B)
C)
D)
E) The integral does not converge.

Question 11

Evaluate the following integral.

A)
B)
C)
D)
E)

Question 12

Evaluate the following iterated integral.

A) 5,901
B) 5,931
C) 5,955
D) 5,970
E) 6,017

Question 13

Sketch the region R of integration and then switch the order of integration for the following integral.

A)
B)
C)
D)
E)

Question 14

Evaluate the following iterated integral.

A) 41.5
B) 38.5
C) 34.5
D) 33.5
E) 37.5

Question 15

Evaluate the iterated integral below. Note that it is necessary to switch the order of integration.

A)
B)
C)
D)
E)

Question 16

Use an iterated integral to find the area of the region bounded by .

A)
B)
C)
D)
E)

Question 17

The area of a region R is given by the iterated integral . Switch the order of integration and show that both orders yield the same area. What is this area?

A) 65
B) 16
C) 21
D) 8
E) 4

Question 18

Use an iterated integral to find the area of the region bounded by the graphs of the equations and .

A)
B)
C)
D)
E)

Question 19

The area of a region R is given by the iterated integrals . Switch the order of integration and show that both orders yield the same area. What is this area?

A) 32
B) 1025
C) 64
D) 771
E) 63

Question 20

Evaluate the following integral.

A)
B)
C)
D)
E)