Deck 7: Area of a Region Between Two Curves

Question 1

up and evaluate the integral that gives the volume of the solid formed by

Answer 1

E

Question 2

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). Find the area of the face of the
Section superimposed on the rectangular coordinate system. Round your answer to three decimal
Places.

Answer 2

E

Question 3

the area of the region bounded by the graphs of the algebraic functions.

Answer 3

A

Question 4

chief financial officer of a company reports that profits for the past fiscal year were $ million. The officer predicts that profits for the next 7 years will grow at a continuous

Question 5

up the definite integral that gives the area of the region bounded by the graph of

Question 6

the accumulation function

Question 7

the area of the region bounded by the graphs of the equations.

Question 8

the area of the region bounded by the equations by integrating (i) with respect to x and
(ii) with respect to y.

Question 9

up and evaluate the integral that gives the volume of the solid formed by

Question 10

Question 11

the area of the region bounded by the graphs of the function

Question 12

the area of the region bounded by equations by integrating (i) with respect to x and
(ii) with respect to y.

Question 13

the area of the region bounded by the graphs of the algebraic functions.

Question 14

the area of the region bounded by the graphs of the algebraic functions.

Question 15

the area of the region bounded by the graphs of the algebraic functions.

Question 16

the area of the region bounded by the graphs of the function

Question 17

the area of the region bounded by the graphs of the equations.

Question 18

Question 19

Concrete sections for the new building have the dimensions (in meters) and shape as shown in the figure (the picture is not necessarily drawn to scale). One cubic meter of concrete
Weighs 4320 pounds. Find the weight of the section. Round your answer to the nearest pound.
C)216,267 pounds

Question 20

surface of a machine part is the region between the graphs of

Question 21

the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

Question 22

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the

Question 23

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line

Question 24

up and evaluate the integral that gives the volume of the solid formed by revolving the region

Question 25

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the -axis. Verify your results using the integration capabilities of a
Graphing utility.

Question 26

the volume of the solid generated by revolving the region bounded by the

Question 27

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.

Question 28

the volume of the solid generated by revolving the region bounded by the

Question 29

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.

Question 30

the shell method to set up and evaluate the integral that gives the volume of the

Question 31

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line

Question 32

the volume of the solid generated by revolving the region bounded by the

Question 33

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line

Question 34

tank on the wing of a jet aircraft is formed by revolving the region bounded by the

Question 35

tank on a water tower is a sphere of radius 65 feet. Determine the depth of the water when the tank is filled to one-fourth of its total capacity. (Note: Use the zero or root feature of a
Graphing utility after evaluating the definite integral.) Round your answer to two decimal places.

A)20.66 feet
B)54.63 feet
C)34.67 feet
D)42.43 feet
E)10.36 feet

Question 36

the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

Question 37

the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

Question 38

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the

Question 39

the shell method to set up and evaluate the integral volume of the solid generated by revolving the plane region about the y-axis.

Question 40

the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines.

Question 41

[1,64].

Question 42

16].

Question 43

Question 44

Question 45

the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

Question 46

the disk or shell method to find the volume of the solid generated by revolving

Question 47

the arc length of the graph of the function

Question 48

the disk or the shell method to find the volume of the solid generated by

Question 49

solid is generated by revolving the region bounded by about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one-fourth of the volume is removed. Find the diameter of the hole. Round your answer
To three decimal places.

A)10.733
B)11.167
C)4.392
D)2.536
E)8.785

Question 50

the disk or the shell method to find the volume of the solid generated by

Question 51

the integration capabilities of a graphing utility to approximate the arc length of the graph of . Round your answer to three decimal places.

A)3.620
B)5.020
C)10.540
D)3.820
E)5.270

Question 52

Question 53

the disk or shell method to find the volume of the solid generated by revolving the region in the first quadrant bounded by the graph of the equation about the given line.

Question 54

the shell method to set up and evaluate the integral that gives the volume of the

Question 55

the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis.

Question 56

the shell method to find the volume of the solid generated by revolving the plane

Question 57

the disk or the shell method to find the volume of the solid generated by

Question 58

the shell method to find the volume of the solid generated by revolving the plane

Question 59

Question 60

the disk or shell method to find the volume of the solid generated by revolving

Question 61

lunar module weighs 16 tons on the surface of Earth. How much work is done in propelling the module from the surface of the moon to a height of 50 miles? Consider the radius of
The moon to be 1100 miles and its force of gravity to be one-sixth that of Earth.

Question 62

force of 20 pounds stretches a spring 11 inches in an exercise machine. Find the work done in stretching the spring 2 feet from its natural position.

Question 63

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a six-ton satellite to a height of 200 miles above earth. Assume that Earth has a radius of
4000 miles.

Question 64

bridge has a main span of about 1400 meters. Each of its towers has a height of about 146 meters. Approximate the length of a parabolic cable along the main span if the length C of

A)719.8 meters
B)759.4 meters
C)2120.7 meters
D)1439.6 meters
E)2879.2 meters

Question 65

overhead garage door has two springs, one on each side of the door. A force of 12 pounds is required to stretch each spring 1 foot. Because of the pulley system, the springs stretch only
One-half the distance the door travels. The door moves a total of 10 feet and springs are at their
Natural length when the door is open. Find the work done by pair of strings.

A)150 ft-lb
B)300 ft-lb
C)2,400 ft-lb
D)1,200 ft-lb
E)600 ft-lb

Question 66

force of 265 Newtons stretches a spring 20 centimeters. How much work is done in stretching the spring from 15 centimeters to 25 centimeters?

A)28.5 joules
B)31.5 joules
C)26.5 joules
D)21.5 joules
E)36.5 joules

Question 67

the area of the surface generated by revolving the curve about the y-axis.

Question 68

the area of the surface generated by revolving the curve about the x-axis.

Question 69

Determine the work done by lifting a 140 pound bag of sugar 12 feet.

A)1,680 ft-lb
B)16,800 ft-lb
C)2,600 ft-lb
D)168 ft-lb
E)260 ft-lb

Question 70

Electrical wires suspended between two towers form a catenary modeled by the

Question 71

the area of the surface generated by revolving the curve about the y-axis.

Question 72

the area of the surface generated by revolving the curve about the x-axis.

Question 73

up and evaluate the definite integral for the area of the surface formed by

Question 74

about the x-axis where x and y are measured in feet. Approximate the amount of glass needed to make the bulb. (Assume that the glass is 0.016 inches thick.) Round your answer to four decimal places.

Question 75

Round your answer to four decimal places.

A)4.1888
B)0.2618
C)0.1309
D)1.8546
E)2.0944

Question 76

Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 12-ton satellite to a height of 100 miles above Earth. Assume that the Earth has a
Radius of 4000 miles.

A)1,756.10 mi-ton
B)1,170.73 mi-ton
C)702.44 mi-ton
D)936.59 mi-ton
E)2,575.61 mi-ton

Question 77

up and evaluate the definite integral for the area of the surface formed by

Question 78

barn is 75 feet long and 50 feet wide. A cross section of the roof is the inverted

Question 79

tank with a base of 4 feet by 3 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per cubic foot. How much work is done in pumping water out over the top edge
In order to empty half of the tank. Round your answer to one decimal place.

Question 80

force of 10 pounds compresses a 21-inch spring 8 inches. How much work is done in compressing the spring from a length of 15 inches to a length of 13 inches?

A)22.5 ft-lb
B)19.5 ft-lb
C)17.5 ft-lb
D)12.5 ft-lb
E)27.5 ft-lb