Question 1

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 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 an integral formula to evaluate   . ​

Accepted Answer

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

Question 4

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 5

Find the average value of the given function over the given interval. ​

Accepted Answer

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

Question 6

Use integration by parts to evaluate the integral   ​

Accepted Answer

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

Question 7

A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by   (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by   (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Determine which is the better buy by finding the present value of each business over the next 6 years (until the couple reach age 64). ​

Accepted Answer

A)  the Video Palace 
B)  the Gift Shoppe 
A)  the Video Palace 
B)  the Gift Shoppe

Question 8

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 9

If the supply function for x units of a commodity is   dollars, what is the producer's surplus at   ? Round your answer to two decimal places. ​

Accepted Answer

A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84 
A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84

Question 10

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 11

Evaluate   . ​

Accepted Answer

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

Question 12

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 13

In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from   for 2004 to   for 2005. Find the Gini coefficient of income for both years. Round your answer to six decimal places. ​

Accepted Answer

A)  2004: 0.331754
2005: 0.234910 
B)  2004: 0.434783
2005: 0.316194 
C)  2004: 0.268199
2005: 0.186871 
D)  2004: 0.225080
2005: 0.155144 
E)  2004: 0.630631
2005: 0.483492 
A)  2004: 0.331754
2005: 0.234910 
B)  2004: 0.434783
2005: 0.316194 
C)  2004: 0.268199
2005: 0.186871 
D)  2004: 0.225080
2005: 0.155144 
E)  2004: 0.630631
2005: 0.483492

Question 14

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 15

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

Accepted Answer

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

Question 16

Find the area between the curve   and the x-axis from   to   . ​

Accepted Answer

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

Question 17

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 18

Use an integral formula to evaluate   .

Accepted Answer

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

Question 19

Suppose that the income from a slot machine in a casino flows continuously at a rate of   , where t is the time in hours since the casino opened. The total income during the first 8 hours is given by   . Find the average income over the first 8 hours. ​

Accepted Answer

A)  $289.02 
B)  $313.24 
C)  $728.90 
D)  $560.69 
E)  $953.18 
A)  $289.02 
B)  $313.24 
C)  $728.90 
D)  $560.69 
E)  $953.18

Question 20

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

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

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

Use an integral formula to evaluate .

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.

Find the average value of the given function over the given interval.

Use integration by parts to evaluate the integral

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 x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places.

Use integration by parts to evaluate .

Evaluate .

Use integration by parts to evaluate .

In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from for 2004 to for 2005. Find the Gini coefficient of income for both years. Round your answer to six 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.

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

Find the area between the curve and the x-axis from to .

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

Use an integral formula to evaluate .

Suppose that the income from a slot machine in a casino flows continuously at a rate of , where t is the time in hours since the casino opened. The total income during the first 8 hours is given by . Find the average income over the first 8 hours.

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

Linear Equations and Functions

Quadratic and Other Special Functions

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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

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A: Definite Integrals - Techniques

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Exam 13: Definite Integrals - Techniques

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

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

Use an integral formula to evaluate . ​

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. ​

Find the average value of the given function over the given interval. ​

Use integration by parts to evaluate the integral ​

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 x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places. ​

Use integration by parts to evaluate . ​

Evaluate . ​

Use integration by parts to evaluate . ​

In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from for 2004 to for 2005. Find the Gini coefficient of income for both years. Round your answer to six 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. ​

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

Find the area between the curve and the x-axis from to . ​

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

Use an integral formula to evaluate .

Suppose that the income from a slot machine in a casino flows continuously at a rate of , where t is the time in hours since the casino opened. The total income during the first 8 hours is given by . Find the average income over the first 8 hours. ​

Evaluate the integral by integration. Round your answer to two 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

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

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

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

Use an integral formula to evaluate .

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.

Find the average value of the given function over the given interval.

Use integration by parts to evaluate the integral

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 x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to two decimal places.

Use integration by parts to evaluate .

Evaluate .

Use integration by parts to evaluate .

In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from for 2004 to for 2005. Find the Gini coefficient of income for both years. Round your answer to six 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.

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

Find the area between the curve and the x-axis from to .

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

Suppose that the income from a slot machine in a casino flows continuously at a rate of , where t is the time in hours since the casino opened. The total income during the first 8 hours is given by . Find the average income over the first 8 hours.

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