Question 1

Evaluate the given integral with the Fundamental Theorem of Calculus   . ​

Accepted Answer

A)  -26 
B)  -25 
C)  -28 
D)  -35 
E)  -31 
A)  -26 
B)  -25 
C)  -28 
D)  -35 
E)  -31

Question 2

The demand function for a certain product is   and the supply function is   where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

Accepted Answer

A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars 
A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars

Question 3

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 4

Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by   in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424 
A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424

Question 5

Suppose the rate of production of a new line of products is given by   where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced. ​

Accepted Answer

A)  505 units 
B)  695 units 
C)  895 units 
D)  305 units 
E)  495 units 
A)  505 units 
B)  695 units 
C)  895 units 
D)  305 units 
E)  495 units

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

The rate of depreciation of a building is given by   dollars per year,   . Use the definite integral to find the total depreciation over the first 20 years. ​

Accepted Answer

A)  $700,000 
B)  $35,000 
C)  ​$350,000 
D)  $200,000 
E)  $1,400,000 
A)  $700,000 
B)  $35,000 
C)  ​$350,000 
D)  $200,000 
E)  $1,400,000

Question 8

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 9

The demand function for a product is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus? ​

Accepted Answer

A)  $1,175 
B)  $1,250 
C)  $1,375 
D)  $1,220 
E)  $1,340 
A)  $1,175 
B)  $1,250 
C)  $1,375 
D)  $1,220 
E)  $1,340

Question 10

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function   . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Accepted Answer

A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609 
A)  0.242 
B)  0.567 
C)  0.391 
D)  0.758 
E)  0.609

Question 11

Find the producer's surplus for a product with demand function   and supply function   where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

Accepted Answer

A)  37.5 million dollars 
B)  26.5 million dollars 
C)  21.0 million dollars 
D)  22.5 million dollars 
E)  23.5 million dollars 
A)  37.5 million dollars 
B)  26.5 million dollars 
C)  21.0 million dollars 
D)  22.5 million dollars 
E)  23.5 million dollars

Question 12

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 13

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 14

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 15

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 16

Consider the following supply and demand schedules, with p in dollars and x as the number of units.  
Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.
​

Accepted Answer

A)  $6,466.67 
B)  $23,333.33 
C)  $16,166.67 
D)  $26,366.67 
E)  $13,133.33 
A)  $6,466.67 
B)  $23,333.33 
C)  $16,166.67 
D)  $26,366.67 
E)  $13,133.33

Question 17

A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined that the probability density function for transmission failure after repair is   , where t is the number of months after repair. What is the probability that a transmission chosen at random will last more than 4 months? Round to 3 decimal places. ​

Accepted Answer

A)  0.116 
B)  0.083 
C)  0.165 
D)  0.182 
E)  0.149 
A)  0.116 
B)  0.083 
C)  0.165 
D)  0.182 
E)  0.149

Question 18

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 19

Evaluate the integral   . ​

Accepted Answer

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

Question 20

Find the value of the sum   , if   . ​

Accepted Answer

A)  64 
B)  60 
C)  20 
D)  8 
E)  32 
A)  64 
B)  60 
C)  20 
D)  8 
E)  32

Evaluate the given integral with the Fundamental Theorem of Calculus .

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

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.

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced.

Evaluate the integral .

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years.

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.

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus?

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

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

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.

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.

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

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

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.

Evaluate the integral .

Find the value of the sum , if .

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Exam 13: Definite Integrals - Techniques

Evaluate the given integral with the Fundamental Theorem of Calculus . ​

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

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. ​

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced. ​

Evaluate the integral . ​

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years. ​

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. ​

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus? ​

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

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

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. ​

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. ​

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

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables. ​

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. ​

Evaluate the integral . ​

Find the value of the sum , if . ​

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

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Evaluate the given integral with the Fundamental Theorem of Calculus .

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

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.

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced.

Evaluate the integral .

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years.

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.

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium price is $40, what is the consumer's surplus?

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

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

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.

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.

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

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

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.

Evaluate the integral .

Find the value of the sum , if .