Deck 6: Additional Integration Topics

Question 1

Solve the problem.
The Lorenz curve for the income distribution in a certain country is given by I) Find the Gini index of income concentration. II) Use the answer found in I) to determine if the income of this country is more equally distributed, less equally
Distributed, or distributed the same as a second country having an index of income concentration of 0.2.

A) I) 0.33
B) I) 0.25 II) less equally distributed II) less equally distributed
C) I) 0.25
D) I) 0.33 II) more equally distributed II) more equally distributed

Answer 1

I) 0.25 II) less equally distributed II) less equally distributed

Question 2

Provide an appropriate response.
Find the area bounded by and y = x + 1.

A)
B)
C) 54
D)

Answer 2

Question 3

Solve the problem.
The Lorenz curve for the income distribution in a small country is given by the function Find the Gini index of income concentration. Round the answer to three decimal places.

A) 0.474
B) 0.143
C) 0.263
D) 0.35714

Answer 3

0.474

Question 4

Set up a definite integral that represents the shaded area.

A)
B)
C)
D)

Question 5

Solve the problem.

A) 145.69
B) 6.70
C) 400.71
D) 27.29

Question 6

Set up a definite integral that represents the shaded area.

A)
B)
C)
D)

Question 7

Provide an appropriate response.
Find the area lying above the x-axis and under the parabola . (Round answers to three decimal places.)

A) 32
B) 10.667
C) - 10.667
D) 11

Question 8

Provide an appropriate response.
Find the area bounded by y = 0 for 0 ≤ x ≤ 1.

A) 1
B) 2
C) 3
D) 6

Question 9

Provide an appropriate response.
Find the area between the graph of and the x-axis over the interval (Round answer to two decimal places, if necessary.)

A) 12.13
B) 3.22
C) 20.13
D) 8.97

Question 10

Solve the problem.
The Lorenz curve for the income distribution in a certain country is given by the function . Find the
Gini index of income concentration. Round the answer to three decimal places and interpret the results.

Question 11

Provide an appropriate response.
Find the area between the graph of and the x-axis over the interval [-5, 5]. (Round answer to two decimal places.)

A) 333.33
B) 33.33
C) 666.67
D) 66.67

Question 12

Provide an appropriate response.
Find the area between the graph of f(x) = 50 + and the x-axis over the interval [-2, 4].

A) 372
B) 269
C) 92
D) -92

Question 13

Provide an appropriate response.
Find the area bounded by and g(x) = 2x + 7. (Round answer to two decimal places.)

A) 32.65
B) 20.83
C) 55.83
D) 16.13

Question 14

Provide an appropriate response.
Find the area between the graph of and the x-axis over the interval (Round answer to two decimal places.)

A) 32.33
B) 5.33
C) 27
D) 21.67

Question 15

Solve the problem.

A) 0.99
B) 0.36
C) 147.41
D) 145.69

Question 16

Solve the problem.
The Lorenz curve for the income distribution in a small country is given by the function Find the Gini index of income concentration. Round the answer to three decimal places.

A) -0.584
B) 0.684
C) 0.584
D) 0.292

Question 17

Provide an appropriate response.
Find the area bounded by the parabolas (Round answer to three decimal places.)

A) - 21.333
B) 21.333
C) 21.667
D) 22

Question 18

Provide an appropriate response.
Find the area between the graph of and the x-axis over the interval [1, 3]. (Round answer to two decimal places.)

A) 8.67
B) 10
C) 8
D) - 8.67

Question 19

Provide an appropriate response.
Find the area (to three decimal places) bounded by and

A) 7.676
B) 7.0
C) 7.555
D) 7.333

Question 20

Set up a definite integral that represents the shaded area.

A)
B) x
C)
D)

Question 21

Solve the problem.
The length of telephone calls (in minutes) in a public telephone booth has the probability density function: Determine the probability that a call selected at random will last longer than seven minutes. (Round answer to two decimal places.)

A) 0.42
B) 0.31
C) 0.39
D) 0.54

Question 22

Find the producer's surplus for the following supply function at the given point.
Find the equilibrium price if the price-demand equation is and the price-supply equation

A) $13.00
B) $7.00
C) $60.00
D) $20.00

Question 23

Solve the problem.
The length of telephone calls (in minutes) in a public telephone booth has the probability density function: Determine the probability that a call selected at random will last between 2 and 6 minutes. (Round answer to two decimal places.)

A) 0.95
B) 0.65
C) 0.70
D) 0.35

Question 24

Find the producer's surplus for the following supply function at the given point.
Find the equilibrium quantity if the price-demand equation is , and the price-supply equation is

A) -600, 200
B) 200
C) -600
D) 13

Question 25

Solve the problem.
The rate of flow of income from a continuous income stream is given by Find the future value of this income stream at 8% compounded continuously for six years. (Round answer to the nearest dollar.)

A) $2743
B) $2706
C) $14,286
D) $4375

Question 26

Solve the problem.
Find the total income produced by a continuous income stream in the first nine years if the rate of flow is f(t) = 3300.

A) $27,000
B) $9900
C) $18,000
D) $29,700

Question 27

Find the consumer's surplus for the following demand function at the given point.

A) $3.25
B) $7.28
C) $4.50
D) $4.33

Question 28

Solve the problem.
Find the total income produced by a continuous income stream in the first nine years if the rate of flow is f(t) =5000.

A) $4500
B) $22.500
C) $90,000
D) $45,000

Question 29

Find the producer's surplus for the following supply function at the given point.
Find the producers' surplus at a price level of for the price-supply equation

Question 30

Solve the problem.
Find the future value at 9% interest compounded continuously for five years for the continuous income stream with rate of flow f(t) = 750. (Round answer to the nearest dollar.)

A) $750
B) $4736
C) $474
D) $47,359

Question 31

Solve the problem.

A) 70.04
B) 23.19
C) 77.89
D) 53.64

Question 32

Solve the problem.
The rate of flow of a continuous income stream (in thousands of dollars per day) is given by Find the total income produced during the first ten days of operation.

A) $58,874.14
B) $2843.18
C) $239.79
D) $2397.90

Question 33

Solve the problem.
Find the interest earned at 5% compounded continuously for two years by a continuous income stream with rate flow of f(t) = 1250. (Round answer to the nearest dollar.)

A) $22,621
B) $2629
C) $129
D) $2379

Question 34

Find the consumer's surplus for the following demand function at the given point.
Find the consumers' surplus at a price level of for the price-demand equation

A) $4050
B) $720
C) $405
D) $29,250

Question 35

Solve the problem.
Find the future value at 8% interest compounded continuously for five years for the continuous income stream with rate of flow f(t) = 560. (Round answer to the nearest dollar.)

A) $3443
B) $835
C) $2308
D) $2750

Question 36

Find the equilibrium point.

A)
B)
C)
D)

Question 37

Solve the problem.
The life expectancy (in years) of a certain type of computer chip is a continuous random variable with probability density function: Find the probability that a randomly selected chip will last from three to seven years. (Round answer to two decimal
Places.)

A) 0.33
B) 0.21
C) 0.36
D) 0.57

Question 38

Solve the problem.
The rate of flow of a continuous income stream (in thousands of dollars per day) is given by Find the total income produced during the first thirty days of operation.

A) $343.40
B) $34.34
C) $3433.99
D) $34,339.87

Question 39

Find the producer's surplus for the following supply function at the given point.

A) $2
B) -$0.67
C) -$2
D) $0.67

Question 40

Solve the problem.
Find the total income produced by a continuous income stream in the first four years if the rate of flow is f(t) = 500e0.03t. (Round answer to the nearest dollar.)

A) $2125
B) $18,792
C) $564
D) $2486

Question 41

Find the producer's surplus for the following supply function at the given point.
Find the equilibrium price and quantity,producers' surplus for

A)
B)
C)
D)

Question 42

Evaluate using integration by parts.

A)
B)
C)
D)

Question 43

Evaluate using integration by parts.

A)
B)
C)
D)

Question 44

Evaluate using integration by parts.

A)
B)
C)
D)

Question 45

Evaluate using integration by parts.

A)
B)
C)
D)

Question 46

Find the producer's surplus for the following supply function at the given point.
Find the consumers' surplus and producers' surplus for

A)
B)
C)
D)

Question 47

Evaluate using integration by parts.

A) 2.8588
B) 5.0213
C) 1.4597
D) 14.2939

Question 48

Solve the problem.
The rate of water usage for a business, in gallons per day, is given by where t = the number of hours since midnight. Approximately how many gallons of water does the business use in the first 5 hours of
The day?

A) 674 gallons
B) 622 gallons
C) 26 gallons
D) 631 gallons

Question 49

Evaluate using integration by parts.

A) 9.48
B) 40.2
C) 6.70
D) 55.2

Question 50

Evaluate using integration by parts.

A)
B)
C)
D)

Question 51

Illustrate the integral graphically and describe what the integral represents in terms of areas.

A)
B)
C)
D)

Question 52

Evaluate using integration by parts.

A) 0.94
B) 0.39
C) -1.33
D) -2.27

Question 53

Evaluate using integration by parts.

A)
B)
C)
D)

Question 54

Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and the x
axis over that interval. Find the answer to two decimal places.

A) 8.28
B) 10.42
C) 2.14
D) -6.14

Question 55

Solve the problem.
After a person takes a pill, the drug contained in the pill is assimilated into the bloodstream. The rate of assimilation minutes after taking the pill is Find the total amount of the drug that is assimilated
Into the bloodstream during the first 15 minutes after the pill is taken. Round your answer to 2 decimal places.

A) 6.25
B) 0.23
C) 0.38
D) 6.14

Question 56

Evaluate using integration by parts.

A)
B)
C)
D)

Question 57

Use a graphing calculator to graph the equation over the indicated interval and find the area between the curve and the x
axis over that interval. Find the answer to two decimal places.

A) 37.27
B) -35.17
C) -36.22
D) 1.05

Question 58

Evaluate using integration by parts.

A)
B)
C)
D)

Question 59

Illustrate the integral graphically and describe what the integral represents in terms of areas.

A)
B)
C)
D)

Question 60

Evaluate using integration by parts.

A)
B)
C)
D)

Question 61

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 62

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Write answer as whole number or reduced fraction.

A) 18
B) 36
C) 9
D) 15

Question 63

Provide an appropriate response.
Use the integral table to find

A)
B)
C)
D)

Question 64

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Round to two decimal places.

A) 1.11
B) 1.03
C) 1.13
D) 1.21

Question 65

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Round to two decimal places.

A) 1.20
B) 1.29
C) 1.46,
D) 1.33

Question 66

Use the Trapezoidal Rule to approximate the integral using the indicated value of n.
Write answer as a whole number or reduced fraction.

A)
B) 33
C) 16
D)

Question 67

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Write answer as whole number or reduced fraction.

A)
B)
C)
D)

Question 68

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Round to two decimal places.

A) 0.30
B) 0.24
C) 0.20
D) 0.34

Question 69

Use the Trapezoidal Rule to approximate the integral using the indicated value of n.
Round to two decimal places.

A) 1.62
B) 1.12
C) 1.02
D) 1.42

Question 70

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 71

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 72

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
Round to two decimal places.

A) 1.33
B) 1.24
C) 1.10
D) 0.89

Question 73

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 74

Use the Trapezoidal Rule to approximate the integral using the indicated value of n.
Round to three decimal places.

A) 9.908
B) 4.954
C) 2.477
D) 3.108

Question 75

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 76

Use the Trapezoidal Rule to approximate the integral using the indicated value of n.
, Write answer as a whole number or reduced fraction.

A) 92
B) 46
C)
D) 23

Question 77

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)

Question 78

Provide an appropriate response.
Use an integral table to find

A)
B)
C)
D)

Question 79

Use Simpson's rule to approximate the integral using the indicated value of n (so there are 2n subintervals).
, Round to three decimal places.

A) 7.041
B) 7.413
C) 6.328
D) 7.741

Question 80

Find the indefinite integral using a table of integration formulas.

A)
B)
C)
D)