Question 1

Evaluate   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

Find the shaded area between the given function and the x-axis. ​     ​

Accepted Answer

A)  ​   
B)    
C)    
D)    
E)    
A)  ​   
B)    
C)    
D)    
E)

Question 3

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.   ​ ​

Accepted Answer

A)  1.905 
B)  2.858 
C)  4.858 
D)  8.001 
E)  9.716 
A)  1.905 
B)  2.858 
C)  4.858 
D)  8.001 
E)  9.716

Question 4

Find the area, if it exists, of the region under the graph of   and to the right of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 5

The supply function for a good is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Accepted Answer

A)  $88.40 
B)  $40.00 
C)  $28.89 
D)  $78.00 
E)  $52.00 
A)  $88.40 
B)  $40.00 
C)  $28.89 
D)  $78.00 
E)  $52.00

Question 6

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the right-hand endpoints of the subintervals. Compute the approximate area using up to four decimal places as needed. ​   from   to     subintervals.
​

Accepted Answer

A)  9.25 square units 
B)  17.5 square units 
C)  0.5 square unit 
D)  21 square units 
E)  37 square units 
A)  9.25 square units 
B)  17.5 square units 
C)  0.5 square unit 
D)  21 square units 
E)  37 square units

Question 7

Use the Trapezoidal Rule to approximate   with n = 6. Round your answer to two decimal places. ​

Accepted Answer

A)  1091.56 
B)  323.56 
C)  545.78 
D)  212.44 
E)  444.44 
A)  1091.56 
B)  323.56 
C)  545.78 
D)  212.44 
E)  444.44

Question 8

Equations are given whose graphs enclose a region. Find the area of the region. ​

Accepted Answer

A)    
B)  ​   
C)    
D)    
E)    
A)    
B)  ​   
C)    
D)    
E)

Question 9

Suppose that the demand function for an appliance is   where q is the number of units and p is in dollars. What is the consumer's surplus if the equilibrium price is $17.6 and the equilibrium quantity is 21? Round your answer to the nearest dollar. ​

Accepted Answer

A)  $473 
B)  $475 
C)  $811 
D)  $848 
E)  $474 
A)  $473 
B)  $475 
C)  $811 
D)  $848 
E)  $474

Question 10

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow   where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place. ​

Accepted Answer

A)  41,776.7 thousand dollars 
B)  99,623.7 thousand dollars 
C)  42,023.7 thousand dollars 
D)  61,203.7 thousand dollars 
E)  118,823.7 thousand dollars 
A)  41,776.7 thousand dollars 
B)  99,623.7 thousand dollars 
C)  42,023.7 thousand dollars 
D)  61,203.7 thousand dollars 
E)  118,823.7 thousand dollars

Question 11

Use the figure to decide which of   is larger, or if they are equal. ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 12

Find the area of the shaded region for the graph given below. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Use an integral formula to evaluate   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

The demand function for a product is   , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places. ​

Accepted Answer

A)  $22.86 
B)  $28.24 
C)  $48.00 
D)  $62.40 
E)  $115.20 
A)  $22.86 
B)  $28.24 
C)  $48.00 
D)  $62.40 
E)  $115.20

Question 15

Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by   in thousands of dollars per year. Find the total income from the machines predicted by the model over the first 5 years. Round your answer to the nearest thousand dollars. ​

Accepted Answer

A)  $29,743,000 
B)  $592,000 
C)  $743,000 
D)  $897,000 
E)  $29,592,000 
A)  $29,743,000 
B)  $592,000 
C)  $743,000 
D)  $897,000 
E)  $29,592,000

Question 16

Evaluate the definite integral   . ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

The manufacturer of a medicine wants to test how a new 300-milligram capsule is released into the bloodstream. After a volunteer is given a capsule, blood samples are drawn every half-hour, and the number of milligrams of the drug in the bloodstream is calculated. The results obtained are as follows.  
Use the trapezoidal rule to approximate the average number of milligrams in the bloodstream during the first   hours and round your answer to two decimal places.
​

Accepted Answer

A)  433.60 mg 
B)  197.09 mg 
C)  123.18 mg 
D)  256.22 mg 
E)  335.05 mg 
A)  433.60 mg 
B)  197.09 mg 
C)  123.18 mg 
D)  256.22 mg 
E)  335.05 mg

Question 18

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Accepted Answer

A)    
B)  2 
C)  4 
D)    
E)  3 
A)    
B)  2 
C)  4 
D)    
E)  3

Question 19

If the supply function for a commodity is   where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

Accepted Answer

A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars 
A)  5,623 million dollars 
B)  3,461 million dollars 
C)  3,468 million dollars 
D)  3,999 million dollars 
E)  3,524 million dollars

Question 20

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by   , where   represents 1990. Evaluate   . Round your answer to the nearest cent. ​

Accepted Answer

A)  $1,358.51 
B)  $15,558.45 
C)  $93,350.70 
D)  $10,372.30 
E)  $51,861.50 
A)  $1,358.51 
B)  $15,558.45 
C)  $93,350.70 
D)  $10,372.30 
E)  $51,861.50

Evaluate .

Find the shaded area between the given function and the x-axis.

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.

Find the area, if it exists, of the region under the graph of and to the right of .

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the right-hand endpoints of the subintervals. Compute the approximate area using up to four decimal places as needed. from to subintervals.

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Equations are given whose graphs enclose a region. Find the area of the region.

Suppose that the demand function for an appliance is where q is the number of units and p is in dollars. What is the consumer's surplus if the equilibrium price is $17.6 and the equilibrium quantity is 21? Round your answer to the nearest dollar.

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place.

Use the figure to decide which of is larger, or if they are equal.

Find the area of the shaded region for the graph given below.

Use an integral formula to evaluate .

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places.

Evaluate the definite integral .

Find the area of the shaded region. Round to the nearest hundredth if necessary.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent.

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 13: Definite Integrals - Techniques

Evaluate . ​

Find the shaded area between the given function and the x-axis. ​ ​

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places. ​ ​

Find the area, if it exists, of the region under the graph of and to the right of .

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places. ​

Equations are given whose graphs enclose a region. Find the area of the region. ​

Suppose that the demand function for an appliance is where q is the number of units and p is in dollars. What is the consumer's surplus if the equilibrium price is $17.6 and the equilibrium quantity is 21? Round your answer to the nearest dollar. ​

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place. ​

Use the figure to decide which of is larger, or if they are equal. ​

Find the area of the shaded region for the graph given below. ​ ​

Use an integral formula to evaluate . ​

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places. ​

Evaluate the definite integral . ​

Find the area of the shaded region. Round to the nearest hundredth if necessary.

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars. ​

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent. ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Evaluate .

Find the shaded area between the given function and the x-axis.

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.

The supply function for a good is , where p is the number of dollars and x is the number of units. If the equilibrium price is $27 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Equations are given whose graphs enclose a region. Find the area of the region.

Suppose that the demand function for an appliance is where q is the number of units and p is in dollars. What is the consumer's surplus if the equilibrium price is $17.6 and the equilibrium quantity is 21? Round your answer to the nearest dollar.

Suppose that when a new oil well is opened, its production is viewed as a continuous income stream with monthly rate of flow where t is time in months and f is in thousands of dollars per month. Find the total income over the next 40 years (480 months). Round your answer to one decimal place.

Use the figure to decide which of is larger, or if they are equal.

Find the area of the shaded region for the graph given below.

Use an integral formula to evaluate .

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places.

Evaluate the definite integral .

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus when 12 thousand units are sold? Round your answer to the nearest million dollars.

Market revenue for Hammer Inc. (in millions of dollars per year) can be modeled by , where represents 1990. Evaluate . Round your answer to the nearest cent.