Deck 5: Integration

Question 1

Solve the problem.
The rate of change in a person's body temperature, with respect to the dosage of x milligrams of a drug, is given by One milligram raises the temperature 3.5°C. Find the function giving the total change.

A)
B)
C)
D)

Answer 1

Question 2

Find the integral.

A)
B)
C)
D)

Answer 2

Question 3

Find the integral.

A)
B) 0
C) 3 + C
D) 3x + C

Answer 3

3x + C

Question 4

Find the integral.

A)
B)
C)
D)

Question 5

Find the integral.

A)
B)
C)
D)

Question 6

Solve the problem.
Find the cost function if the marginal cost function is and the fixed cost is $14.

A)
B)
C)
D)

Question 7

Find the integral.

A)
B)
C)
D)

Question 8

Provide an appropriate response.
Find f(x) if

A)
B)
C)
D)

Question 9

Find the integral.

A)
B)
C)
D)

Question 10

Find the integral.

A)
B)
C)
D)

Question 11

Find the integral.

A)
B)
C)
D)

Question 12

Find the integral.

A)
B)
C)
D)

Question 13

Provide an appropriate response.

A)
B)
C)
D)

Question 14

Find the integral.

A)
B)
C)
D)

Question 15

Find the integral.
.

A)
B)
C)
D)

Question 16

Find the integral.

A)
B)
C)
D)

Question 17

Find the integral.

A)
B)
C) 10t - 5 + C
D)

Question 18

Find the integral.

A)
B)
C)
D)

Question 19

Solve the problem.
A company finds that consumer demand quantity changes with respect to price at a rate given by Find the demand function if the company knows that 842 units of the product are demanded when the price is $5 per unit.

A)
B)
C)
D)

Question 20

Find the integral.

A)
B)
C)
D)

Question 21

Solve the problem.
The rate of expenditure for maintenance of a particular machine is given by where x is time measured in years. Total maintenance costs through the second year are $105. Find the total maintenance
Function.

A)
B)
C)
D)

Question 22

Find the integral.

A)
B)
C)
D)

Question 23

Find the integral.

A)
B)
C)
D)

Question 24

Find the integral.

A)
B)
C)
D)

Question 25

Find the integral.

A)
B)
C)
D)

Question 26

Solve the problem.
An rock's acceleration at time t is given by a(t) = 16t, and its initial velocity is 35. Find the velocity function v(t).

A)
B)
C)
D)

Question 27

Solve the problem.
A computer manufacturer has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by where x is the number of days since the start of the job. Find the expenditure if
The job takes 8 days.

A) $36,800
B) $86
C) $368
D) $8600

Question 28

Solve the problem.
A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive test marketing, the market research department estimates that sales (in millions of dollars) will increase at the
Monthly rate of months after the national campaign has started. What will the
Total sales be five months after the beginning of the campaign if we assume zero sales at the beginning of the
Campaign? (Round the answer to the nearest million.)

A) $49 million
B) $1 million
C) $2 million
D) $18 million

Question 29

Solve the problem.
A company has found that the marginal cost of a new production line (in thousands) is where x is the number of years the line is in use. Find the total cost function for the production line (in thousands). The
Fixed cost is $20,000.

A)
B) C(x) = 9 ln (x + e) + 20
C)
D) C(x) = 9 ln (x + e) + 11

Question 30

Solve the problem.
The marginal price for a weekly demand of x bottles of cough medicine in a drug store is given by . Find the price-demand equation if the weekly demand is 125 when the price of a bottle of cough medicine is $4. What is the weekly demand (to the nearest bottle) when the price is $3?

A)
B)
C)
D)

Question 31

Find the integral.

A)
B)
C)
D)

Question 32

Solve the problem.
A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The newspaper currently (t = 0) has 26,000 daily subscribers and management expects that number, S(t), to
Grow at the rate of 2 subscribers per day, where t is the number of days since the campaign began.
How long (to the nearest day) should the campaign last if the newspaper wants the number of daily subscribers
To grow to 49,000?

A) 57 days
B) 69 days
C) 44 days
D) 33 days

Question 33

Solve the problem.
The marginal revenue from the sale of compact discs is given by where R(x) is the revenue in dollars. Find the price-demand equation.

A)
B) p = 190x - 8
C) p = 190 - 4x
D)

Question 34

Find the integral.

A)
B)
C)
D)

Question 35

Find the integral.

A)
B)
C)
D)

Question 36

Find the integral.

A)
B)
C)
D)

Question 37

Find the integral.

A)
B)
C)
D)

Question 38

Find the integral.

A)
B)
C)
D)

Question 39

Find the integral.

A)
B)
C)
D)

Question 40

Solve the problem.
The management of an oil company estimates that oil will be pumped from a producing field at a rate given by where R(t) is the rate of production in thousands of barrels per year, t years after pumping begins. How many barrels of oil, Q(t), will be produced the first five years? (Round answer to the
Nearest thousand barrels.)

A) 296 thousand barrels
B) 92 thousand barrels
C) 46 thousand barrels
D) 148 thousand barrels

Question 41

Solve the problem.
At the beginning of an advertising campaign for a new product in a city of 500,000 people, no one is aware of the product. After 10 days, 100,000 people are aware of the product. If N = N(t) is the number of people (in
Thousands) who are aware of the product t days after the beginning of the advertising campaign, solve the
Following differential equation for N(t):

A)
B)
C)
D)

Question 42

Match the differential equation with the appropriate slope field.

A)
B)
C)
D)

Question 43

Provide an appropriate response.
Find the general solution for the differential equation y

A)
B)
C)
D)

Question 44

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

A) right rectangles
B) left rectangles
C) neither

Question 45

Solve the problem.
Find the amount A in an account (to the nearest dollar) after 5 years if

A) $1000
B) $1200
C) $1100
D) $919

Question 46

Solve the problem.
A single injection of a drug is administered to a patient. The amount Q in the body then decreases at a rate proportional to the amount present, and for this particular drug the rate is 3% per hour. Thus, with where t is time in hours. If the initial injection is 4 milliliters about how many hours
After the drug is given will there be 2 milliliters of the drug remaining in the body? (Round answer to the
Nearest tenth of an hour.)

A) 69.3 hours
B) 21.3 hours
C) 11.3 hours
D) 23.1 hours

Question 47

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

A) left rectangles
B) right rectangles
C) neither

Question 48

Solve the problem.
If the marginal price units of demand per week is proportional to the price p, and if at $80 there is no weekly demand [p(0) = 80], and if at $50.18 there is a weekly demand of 8 units [p(8) = 50.18], find the
Price-demand equation.

A)
B)
C)
D)

Question 49

Provide an appropriate response.
Find the particular solution for the differential equation

A)
B)
C)
D)

Question 50

Provide an appropriate response.
Graph the following example of exponential decay:

A)
B)
C)
D)

Question 51

Match the differential equation with the appropriate slope field.

A)
B)
C)
D)

Question 52

Match the differential equation with the appropriate slope field.

A)
B)
C)
D)

Question 53

Provide an appropriate response.
Find the general solution for the differential equation

A)
B)
C)
D)

Question 54

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

A) right rectangles
B) neither
C) left rectangles

Question 55

Provide an appropriate response.
Find the particular solution for the differential equation

A)
B)
C)
D)

Question 56

Provide an appropriate response.
Find the general solution for the differential equation

A)
B)
C)
D)

Question 57

Provide an appropriate response.
Graph the following example of unlimited growth:

A)
B)
C)
D)

Question 58

Provide an appropriate response.
Find the particular solution for the differential equation

A)
B)
C)
D)

Question 59

Match the differential equation with the appropriate slope field.

A)
B)
C)
D)

Question 60

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

A) right rectangles
B) neither
C) left rectangles

Question 61

Solve the problem.
A factory discharges pollutants into a large river at a rate that is estimated by a water quality control agency to be where P(t) is the total number of tons of pollutants discharged into the river after t
Years of operation. What quantity of pollutants will be discharged into the river from the end of the third year to
The end of the fifth year? (Round to two decimal places.)

A) 33.65 tons
B) 32.67 tons
C) 50.67 tons
D) 75.71 tons

Question 62

Provide an appropriate response.
How large should n (n an integer) be chosen for Ln and Rn for the approximation of (ln x + 1) dx to be within 0.05 of the true value?

A)
B)
C)
D)

Question 63

Evaluate the integral.
(Round to three decimal places.)

A) 3.001
B) 12.846
C) 7.505
D) 1.410

Question 64

Evaluate the integral.

A) -7
B) 12
C) 7
D) 2

Question 65

Evaluate the integral.

A)
B)
C)
D)

Question 66

Evaluate the integral.
(Round to three decimal places.)

A) 2.510
B) 0.967
C) 5.021
D) 0.425

Question 67

Provide an appropriate response.
Given

A) 2
B) 30
C) 26
D) 28

Question 68

Provide an appropriate response.
Calculate the Riemann sum, , for the function on the interval [-3, 7]. Partition [-3, 7] into five subintervals of equal length and for each subinterval be the midpoint.

A) - 40
B) 40
C) 38
D) -38

Question 69

Provide an appropriate response.
Divide the interval [0, 8] into four equal subintervals and draw in the corresponding left rectangles.

A)
B)
C)
D)

Question 70

Evaluate the integral.
(Express your answer in terms for e.)

A)
B)
C)
D)

Question 71

Provide an appropriate response.
Given that find the definite integral

A)
B) - 6
C)
D)

Question 72

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
f(x) = from x = 1 to x = 5; n = 4; compute R4

A) 150
B) 144
C) 140
D) 154

Question 73

Provide an appropriate response.
(A) Calculate the change in F(x) from x = 3 to x = 7.
(B) Graph and use geometric formulas to calculate the area between the graph of and the x-axis from
x = 3 to x = 7.
(C) What guarantees that your answers to (A) and (B) are equal?

Question 74

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
f(x) = interval [0, 5]; n = 5; compute L5

A) 32
B) 40
C) 65
D) 66

Question 75

Evaluate the integral.

A) 192
B) 288
C) 24
D) 128

Question 76

Provide an appropriate response.
Divide the interval [0, 8] into four equal subintervals and draw in the corresponding right rectangles.

A)
B)
C)
D)

Question 77

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
f(x) = 2x + 3 from x = 0 to x = 2; n = 4; compute R4

A) 13
B) 11
C) 17
D) 15

Question 78

Provide an appropriate response.
Given use properties of definite integrals to evaluate

A) 18
B) 24
C) 13
D) 54

Question 79

Evaluate the integral.
(Round to three decimal places.)

A) 1.199
B) 2.398
C) 1.778
D) 1.040

Question 80

Solve the problem.
Test marketing for a new health-food snack product in a selected area suggests that sales (in thousands of dollars) will increase at a rate given by t months after an aggressive national advertising
Campaign is begun. Find total sales during the second 12 months of the campaign. (Round to the nearest
Thousand dollars.)

A) $267,000
B) $511,000
C) $693,000
D) $449,000