Deck 14: Iterated Integrals and Area in the Plane

Question 1

order of integration and show that both orders yield the same area. What is this area?

Answer 1

C

Question 2

Evaluate the following iterated integral.

Answer 2

A

Question 3

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

Answer 3

A

Question 4

integration. Round your answer to three decimal places.

Question 5

Evaluate the following iterated integral.

Question 6

Evaluate the following integral.

Question 7

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

Question 8

A)3
B)8
C)6
D)9
E)5

Question 9

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

Question 10

Evaluate the following integral.

Question 11

Evaluate the following iterated integral.

Question 12

Evaluate the following integral.

Question 13

Evaluate the following iterated integral.

Question 14

Evaluate the following improper integral.

Question 15

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

Question 16

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

Question 17

of integration and show that both orders yield the same area. What is this area?

Question 18

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?

Question 19

Question 20

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

Question 21

Suppose the temperature in degrees Celsius on the surface of a metal plate is

Question 22

up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations

A)1,089
B)35,937
C)35,949
D)11,979
E)2,178

Question 23

a double integral to find the volume of the indicated solid.

Question 24

Evaluate the double integral below.

Question 25

Combine the sum of the two iterated integrals into a single integral by converting to polar coordinates. Evaluate the resulting iterated integral.

Question 26

a double integral in polar coordinates to find the volume of the solid inside the hemisphere

Question 27

polar coordinates to describe the region as shown in the figure below:

Question 28

Question 29

up and evaluate a double integral to find the volume of the solid bounded by the

Question 30

a double integral to find the volume of the indicated solid.

Question 31

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.

Question 32

up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.

Question 33

Evaluate the double integral below.

Question 34

Find a such that the volume inside the hemisphere

Question 35

a double integral to find the volume of the indicated solid.

Question 36

Evaluate the double integral below.

Question 37

up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations given below.

Question 38

up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.

Question 39

Question 40

a double integral to find the volume of the indicated solid.

Question 41

the center of mass of the rectangular lamina with vertices

Question 42

Determine the diameter of a hole that is drilled vertically through the center of the

Question 43

a double integral to find the area of the shaded region as shown in the figure below.

Question 44

the mass of the lamina described by the inequalities

Question 45

the mass of the lamina described by the inequalities

Question 46

up the double integral required to find the moment of inertia I, about the line

Question 47

a double integral to find the area enclosed by the graph of

Question 48

the center of mass of the lamina bounded by the graphs of the equations

Question 49

the mass of the triangular lamina with vertices the density

A)401k
B)809k
C)800k
D)400k
E)805k

Question 50

the mass of the lamina bounded by the graphs of the equations

Question 51

the center of mass of the lamina bounded by the graphs of the equations

Question 52

a double integral to find the area enclosed by the graph of

Question 53

the mass of the triangular lamina with vertices the density

Question 54

the mass of the lamina bounded by the graphs of the equations

Question 55

up and evaluate a double integral required to find the moment of inertia, I, about the given line, of the lamina bounded by the graphs of the following equations. Use a computer
Algebra system to evaluate the double integral.

Question 56

Suppose the population density of a city is approximated by the model

Question 57

the center of mass of the rectangular lamina with vertices

Question 58

the mass and center of mass of the lamina bounded by the graphs of the equations given below for the given density.

Question 59

the center of mass of the lamina bounded by the graphs of the equations

Question 60

a double integral to find the area of the region inside the circle outside the cardioid

A)46.68
B)58.34
C)20.34
D)55.34
E)22.34

Question 61

Evaluate the following iterated integral.

Question 62

the area of the portion of the surface the region Round your answer to two decimal places.

A)144.00
B)118.44
C)904.78
D)452.39
E)1,421.22

Question 63

company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.

Question 64

the area of the surface given by

Question 65

Write a double integral that represents the surface area of the region R: triangle with vertices . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.

Question 66

the area of the surface for the portion of the paraboloid first
Octant.

Question 67

Question 68

the area of the portion of the surface

Question 69

company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.

Question 70

the area of the surface for the portion of the sphere

Question 71

up a double integral that gives the area of the surface on the graph of

Question 72

Determine the location of the horizontal axis gate in a dam is to be hinged so that there is no moment causing rotation under the indicated loading

Question 73

the area of the surface given by

Question 74

the area of the surface given by

Question 75

the area of the surface of the portion of the plane

Question 76

up a double integral that gives the area of the surface of the graph of f over the region R.

Question 77

the area of the portion of the surface

Question 78

up a double integral that gives the area of the surface of the graph of f over the region R.

Question 79

Determine the location of the horizontal axis for figure (b) at which a vertical

Question 80