Question 1

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 2

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​
 
​

Accepted Answer

A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493 
A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493

Question 3

Evaluate the improper integral if it converges, or state that it diverges. ​   ​

Accepted Answer

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

Question 4

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 5

Find the area of the region enclosed by the graphs of   and   . ​

Accepted Answer

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

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

Evaluate the integral   by integration. Round your answer to two decimal places. ​

Accepted Answer

A)  45.00 
B)  1,192.50 
C)  270.00 
D)  14,310.00 
E)  312.50 
A)  45.00 
B)  1,192.50 
C)  270.00 
D)  14,310.00 
E)  312.50

Question 8

Use integration by parts to evaluate the integral   . Note that evaluation may require integration by parts more than once. ​

Accepted Answer

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

Question 9

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by   in thousands of dollars per year. Find the total income over the next 20 years. ​

Accepted Answer

A)    thousand dollars 
B)    thousand dollars 
C)    thousand dollars 
D)    thousand dollars 
E)    thousand dollars 
A)    thousand dollars 
B)    thousand dollars 
C)    thousand dollars 
D)    thousand dollars 
E)    thousand dollars

Question 10

Evaluate the integral   . ​

Accepted Answer

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

Question 11

Evaluate the definite integral   . ​

Accepted Answer

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

Question 12

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 13

Approximate the area under the curve defined by the function   over the interval x = 0 to x = 3 using the left-hand endpoints of three subintervals (rectangles). ​

Accepted Answer

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

Question 14

Use integration by parts to evaluate   ​

Accepted Answer

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

Question 15

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​   ​

Accepted Answer

A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist 
A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist

Question 16

Find the numerical value of   by using the sum formulas. ​

Accepted Answer

A)  66 
B)  6 
C)  360 
D)  361 
E)  70 
A)  66 
B)  6 
C)  360 
D)  361 
E)  70

Question 17

Evaluate the definite integral   . ​

Accepted Answer

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

Question 18

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by   in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $712,660 
B)  $716,213 
C)  $703,158 
D)  $722,162 
E)  $708,733 
A)  $712,660 
B)  $716,213 
C)  $703,158 
D)  $722,162 
E)  $708,733

Question 19

Find the area of the region enclosed by   and   . ​​

Accepted Answer

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

Question 20

Suppose the number of daily sales of a product was found to be given by   , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from   to   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  $133 
B)  $130 
C)  $127 
D)  $265 
E)  $255 
A)  $133 
B)  $130 
C)  $127 
D)  $265 
E)  $255

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

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Evaluate the improper integral if it converges, or state that it diverges.

Use an integral formula to evaluate .

Find the area of the region enclosed by the graphs of and .

Evaluate the integral .

Evaluate the integral by integration. Round your answer to two decimal places.

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once.

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years.

Evaluate the integral .

Evaluate the definite integral .

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.

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the left-hand endpoints of three subintervals (rectangles).

Use integration by parts to evaluate

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Find the numerical value of by using the sum formulas.

Evaluate the definite integral .

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar.

Find the area of the region enclosed by and .

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar.

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

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

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables. ​ ​

Evaluate the improper integral if it converges, or state that it diverges. ​ ​

Use an integral formula to evaluate . ​

Find the area of the region enclosed by the graphs of and . ​

Evaluate the integral . ​

Evaluate the integral by integration. Round your answer to two decimal places. ​

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once. ​

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years. ​

Evaluate the integral . ​

Evaluate the definite integral . ​

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. ​

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the left-hand endpoints of three subintervals (rectangles). ​

Use integration by parts to evaluate ​

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​ ​

Find the numerical value of by using the sum formulas. ​

Evaluate the definite integral . ​

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar. ​

Find the area of the region enclosed by and . ​​

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar. ​

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

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

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Evaluate the improper integral if it converges, or state that it diverges.

Use an integral formula to evaluate .

Find the area of the region enclosed by the graphs of and .

Evaluate the integral .

Evaluate the integral by integration. Round your answer to two decimal places.

Use integration by parts to evaluate the integral . Note that evaluation may require integration by parts more than once.

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years.

Evaluate the integral .

Evaluate the definite integral .

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.

Approximate the area under the curve defined by the function over the interval x = 0 to x = 3 using the left-hand endpoints of three subintervals (rectangles).

Use integration by parts to evaluate

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Find the numerical value of by using the sum formulas.

Evaluate the definite integral .

A small brewery considers the output of its bottling machine as a continuous income stream with an annual rate of flow at time t given by in thousands of dollars per year. Find the income from this stream for the next 30 years. Round your answer to the nearest dollar.

Find the area of the region enclosed by and .

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar.