Question 1

Evaluate the integral   . ​

Accepted Answer

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

Question 2

Find the producer's surplus for a product if its demand function is   and its supply function is   where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars. ​

Accepted Answer

A)  53 million dollars 
B)  44 million dollars 
C)  40 million dollars 
D)  36 million dollars 
E)  47 million dollars 
A)  53 million dollars 
B)  44 million dollars 
C)  40 million dollars 
D)  36 million dollars 
E)  47 million dollars

Question 3

Evaluate the integral   . ​

Accepted Answer

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

Question 4

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 5

Use Simpson's Rule to approximate   with n = 4. Round your answer to 3 decimal places. ​

Accepted Answer

A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123 
A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123

Question 6

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

Accepted Answer

A)  4.00 
B)  9.79 
C)  0.71 
D)  7.34 
E)  3.77 
A)  4.00 
B)  9.79 
C)  0.71 
D)  7.34 
E)  3.77

Question 7

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 8

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 9

The demand function for a product is   , and the supply function for it is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Accepted Answer

A)  $34.51 
B)  $58.67 
C)  $152.53 
D)  $82.13 
E)  $176.00 
A)  $34.51 
B)  $58.67 
C)  $152.53 
D)  $82.13 
E)  $176.00

Question 10

Use Simpson's Rule to approximate   with n = 4. Round your answer to 2 decimal places. ​

Accepted Answer

A)  5.10 
B)  10.27 
C)  28.17 
D)  5.14 
E)  25.96 
A)  5.10 
B)  10.27 
C)  28.17 
D)  5.14 
E)  25.96

Question 11

The demand function for a product is   and the supply function is   , where p is the number of dollars and x is the number of units. Find the consumer's surplus there. Round to the nearest cent. ​

Accepted Answer

A)  $373.85 
B)  $486.00 
C)  $583.20​ 
D)  $1020.60 
E)  $583.20 
A)  $373.85 
B)  $486.00 
C)  $583.20​ 
D)  $1020.60 
E)  $583.20

Question 12

The Lorenz curve for the income distribution in a certain country in 2005 is given by   . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places. ​

Accepted Answer

A)  ​0.3576 
B)  0.4648 
C)  0.5614 
D)  0.2103 
E)  0.2668 
A)  ​0.3576 
B)  0.4648 
C)  0.5614 
D)  0.2103 
E)  0.2668

Question 13

Find the mean of the probability distribution if the probability density function is   . ​

Accepted Answer

A)  54,000 
B)  2 
C)  60 
D)  30 
E)  90 
A)  54,000 
B)  2 
C)  60 
D)  30 
E)  90

Question 14

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 15

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 16

Use Simpson's Rule to approximate   with n = 4. Round your answer to 3 decimal places. ​

Accepted Answer

A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123 
A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123

Question 17

Use integration by parts to evaluate   ​

Accepted Answer

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

Question 18

Use integration by parts to evaluate   ​

Accepted Answer

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

Question 19

Approximate the given integral by using the Trapezoidal Rule   with n = 4. Round your answer to 3 decimal places. ​

Accepted Answer

A)  0.092 
B)  0.058 
C)  0.068 
D)  0.041 
E)  0.184 
A)  0.092 
B)  0.058 
C)  0.068 
D)  0.041 
E)  0.184

Question 20

Suppose the presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. The group measures the length across the algae growth (see the figure) and obtains the following data (in feet).  
Use 8 rectangles with bases of 10 feet and lengths measured at the left-hand endpoints to approximate the area of the algae growth.   ​
​

Accepted Answer

A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft 
A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft

Evaluate the integral .

Find the producer's surplus for a product if its demand function is and its supply function is where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars.

Evaluate the integral .

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.

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

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.

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.

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Use Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places.

The demand function for a product is and the supply function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus there. Round to the nearest cent.

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places.

Find the mean of the probability distribution if the probability density function is .

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.

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.

Use integration by parts to evaluate

Use integration by parts to evaluate

Approximate the given integral by using the Trapezoidal Rule with n = 4. Round your answer to 3 decimal places.

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

Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

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Filters

Exam 13: A: Definite Integrals - Techniques

Evaluate the integral . ​

Find the producer's surplus for a product if its demand function is and its supply function is where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars. ​

Evaluate the integral . ​

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places. ​

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

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. ​

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. ​

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Use Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places. ​

The demand function for a product is and the supply function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus there. Round to the nearest cent. ​

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places. ​

Find the mean of the probability distribution if the probability density function is . ​

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. ​

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places. ​

Use integration by parts to evaluate ​

Use integration by parts to evaluate ​

Approximate the given integral by using the Trapezoidal Rule with n = 4. Round your answer to 3 decimal places. ​

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

Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Evaluate the integral .

Find the producer's surplus for a product if its demand function is and its supply function is where p is in millions of dollars and x is the number of thousands of units. Round your answer to the nearest million dollars.

Evaluate the integral .

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.

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

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.

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.

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

Use Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places.

The demand function for a product is and the supply function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus there. Round to the nearest cent.

The Lorenz curve for the income distribution in a certain country in 2005 is given by . Find the Gini coefficient of income for 2005 for this country. Round your answer to four decimal places.

Find the mean of the probability distribution if the probability density function is .

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.

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

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.

Use integration by parts to evaluate

Use integration by parts to evaluate

Approximate the given integral by using the Trapezoidal Rule with n = 4. Round your answer to 3 decimal places.