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Deck 14: Section 3: Multiple Integration
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Question
Evaluate the double integral below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere 
but outside the cylinder 
.
A)
B)
C)
D)
E)
but outside the cylinder .A)
B)
C)
D)
E)
Question
Evaluate the following iterated integral by converting to polar coordinates. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use polar coordinates to describe the region as shown in the figure below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations 
if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.
A) 1.2245
B) 31.4490
C) 7.2245
D) 5.4490
E) 15.2245
if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.A) 1.2245
B) 31.4490
C) 7.2245
D) 5.4490
E) 15.2245
Question
Evaluate the double integral below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Given 
use polar coordinates to set up and evaluate the double integral 
.
A)
B)
C)
D)
E)
use polar coordinates to set up and evaluate the double integral .A)
B)
C)
D)
E)
Question
Suppose the population density of a city is approximated by the model 
where x and y are measured in miles. Integrate the density function over the indicated circular region to approximate the population of the city. Round your answer to the nearest integer.
A) 417,127
B) 417,029
C) 833,901
D) 833,903
E) 416,951
where x and y are measured in miles. Integrate the density function over the indicated circular region to approximate the population of the city. Round your answer to the nearest integer.A) 417,127
B) 417,029
C) 833,901
D) 833,903
E) 416,951
Question
Combine the sum of the two iterated integrals into a single integral by converting to polar coordinates. Evaluate the resulting iterated integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double integral to find the area of the region inside the circle 
and outside the cardioid 
. Round your answer to two decimal places.
A) 46.68
B) 58.34
C) 20.34
D) 55.34
E) 22.34
and outside the cardioid . Round your answer to two decimal places.A) 46.68
B) 58.34
C) 20.34
D) 55.34
E) 22.34
Question
Use a double integral in polar coordinates to find the volume of the solid in the first octant bounded by the graphs of the equations given below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find a such that the volume inside the hemisphere 
and outside the cylinder 
is one-half the volume of the hemisphere. Round your answer to four decimal places.
A)
B)
C)
D)
E)
and outside the cylinder is one-half the volume of the hemisphere. Round your answer to four decimal places.A)
B)
C)
D)
E)
Question
Identify the region of integration for the following integral. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double integral to find the area enclosed by the graph of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Evaluate the iterated integral 
by converting to polar coordinates.
A)
B)
C)
D)
E)
by converting to polar coordinates.A)
B)
C)
D)
E)
Question
Evaluate the following iterated integral by converting to polar coordinates. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Evaluate the iterated integral 
by converting to polar coordinates. Round your answer to four decimal places.
A) 10.5742
B) 13.5742
C) 17.5742
D) 28.5742
E) 14.5742
by converting to polar coordinates. Round your answer to four decimal places.A) 10.5742
B) 13.5742
C) 17.5742
D) 28.5742
E) 14.5742
Question
Evaluate the double integral below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double integral to find the area of the shaded region as shown in the figure below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a double integral to find the area enclosed by the graph of 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Deck 14: Section 3: Multiple Integration
1
Evaluate the double integral below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Use a double integral in polar coordinates to find the volume of the solid inside the hemisphere but outside the cylinder .
A)
B)
C)
D)
E)
but outside the cylinder .A)
B)
C)
D)
E)
3
Evaluate the following iterated integral by converting to polar coordinates.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
Use polar coordinates to describe the region as shown in the figure below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
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5
Determine the diameter of a hole that is drilled vertically through the center of the solid bounded by the graphs of the equations if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.
A) 1.2245
B) 31.4490
C) 7.2245
D) 5.4490
E) 15.2245
if one-tenth of the volume of the solid is removed. Round your answer to four decimal places.A) 1.2245
B) 31.4490
C) 7.2245
D) 5.4490
E) 15.2245
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
6
Evaluate the double integral below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
7
Given use polar coordinates to set up and evaluate the double integral .
A)
B)
C)
D)
E)
use polar coordinates to set up and evaluate the double integral .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
8
Suppose the population density of a city is approximated by the model where x and y are measured in miles. Integrate the density function over the indicated circular region to approximate the population of the city. Round your answer to the nearest integer.
A) 417,127
B) 417,029
C) 833,901
D) 833,903
E) 416,951
where x and y are measured in miles. Integrate the density function over the indicated circular region to approximate the population of the city. Round your answer to the nearest integer.A) 417,127
B) 417,029
C) 833,901
D) 833,903
E) 416,951
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
9
Combine the sum of the two iterated integrals into a single integral by converting to polar coordinates. Evaluate the resulting iterated integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
10
Use a double integral to find the area of the region inside the circle and outside the cardioid . Round your answer to two decimal places.
A) 46.68
B) 58.34
C) 20.34
D) 55.34
E) 22.34
and outside the cardioid . Round your answer to two decimal places.A) 46.68
B) 58.34
C) 20.34
D) 55.34
E) 22.34
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
11
Use a double integral in polar coordinates to find the volume of the solid in the first octant bounded by the graphs of the equations given below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
12
Find a such that the volume inside the hemisphere and outside the cylinder is one-half the volume of the hemisphere. Round your answer to four decimal places.
A)
B)
C)
D)
E)
and outside the cylinder is one-half the volume of the hemisphere. Round your answer to four decimal places.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
13
Identify the region of integration for the following integral.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
14
Use a double integral to find the area enclosed by the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
15
Evaluate the iterated integral by converting to polar coordinates.
A)
B)
C)
D)
E)
by converting to polar coordinates.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
16
Evaluate the following iterated integral by converting to polar coordinates.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
17
Evaluate the iterated integral by converting to polar coordinates. Round your answer to four decimal places.
A) 10.5742
B) 13.5742
C) 17.5742
D) 28.5742
E) 14.5742
by converting to polar coordinates. Round your answer to four decimal places.A) 10.5742
B) 13.5742
C) 17.5742
D) 28.5742
E) 14.5742
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
18
Evaluate the double integral below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
19
Use a double integral to find the area of the shaded region as shown in the figure below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 20 flashcards in this deck.
Unlock Deck
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20
Use a double integral to find the area enclosed by the graph of .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 20 flashcards in this deck.
