Question 1

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 2

Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places.   where a = 300, b = 200, c = 400 ​
 
​

Accepted Answer

A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft 
A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft

Question 3

Use the table of values to approximate   Use Simpson's Rule and round your answers to one decimal place. ​

Accepted Answer

A)  82.2 
B)  41.1 
C)  27.4 
D)  13.7 
E)  4.6 
A)  82.2 
B)  41.1 
C)  27.4 
D)  13.7 
E)  4.6

Question 4

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 5

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 6

Use the function   from   to   and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

Accepted Answer

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

Question 7

For a certain product, the total revenue is given by   , and the total cost is given by   . Write an integral that gives the average profit for the product over the interval from 4 to 11 ​

Accepted Answer

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

Question 8

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. Find the present value of the Video Palace over the next 8 years (until the couple reach age 66). Round your answer to the nearest dollar. ​

Accepted Answer

A)  $222,961 
B)  $220,268 
C)  $202,618 
D)  $237,342 
E)  $181,863 
A)  $222,961 
B)  $220,268 
C)  $202,618 
D)  $237,342 
E)  $181,863

Question 9

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 10

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 11

Suppose the Gini coefficient of income for a certain country is   If the Lorenz curve for this country is   , find the value of p. ​

Accepted Answer

A)  12 
B)  11 
C)  10 
D)  ​13 
E)  14 
A)  12 
B)  11 
C)  10 
D)  ​13 
E)  14

Question 12

Suppose the marginal cost for x units of a good is   (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

Accepted Answer

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

Question 13

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 14

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

Accepted Answer

A)  $8,229 
B)  $1,969 
C)  $3,741 
D)  $1,559 
E)  $2,730 
A)  $8,229 
B)  $1,969 
C)  $3,741 
D)  $1,559 
E)  $2,730

Question 15

Assume that the tax burden per capita (in dollars) for selected years from 1950 to 2002 can be modeled by   where   represents 1950. If the model remains valid, find the predicted average federal tax burden per capita from 2000 to 2010. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $8,982 federal tax per capita 
B)  $9,881 average federal tax per capita 
C)  $19,117 average federal tax per capita 
D)  $21,241 average federal tax per capita 
E)  $10,978 average federal tax per capita 
A)  $8,982 federal tax per capita 
B)  $9,881 average federal tax per capita 
C)  $19,117 average federal tax per capita 
D)  $21,241 average federal tax per capita 
E)  $10,978 average federal tax per capita

Question 16

Evaluate the integral   . ​

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Evaluate the integral   . ​

Accepted Answer

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

Question 19

Use the function   from   to   and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find   by using the formula for the sum of the areas of the n rectangles. ​

Accepted Answer

A)  10 
B)  30 
C)  60 
D)  12 
E)  14 
A)  10 
B)  30 
C)  60 
D)  12 
E)  14

Question 20

If the marginal cost function for x units of a product is   dollars per unit, and if the fixed cost is $120, find the total cost function. ​

Accepted Answer

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

Find the numerical value of by using the sum formulas.

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

Use an integral formula to evaluate .

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

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11

Use an integral formula to evaluate .

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

Suppose the Gini coefficient of income for a certain country is If the Lorenz curve for this country is , find the value of p.

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

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

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

Assume that the tax burden per capita (in dollars) for selected years from 1950 to 2002 can be modeled by where represents 1950. If the model remains valid, find the predicted average federal tax burden per capita from 2000 to 2010. Round your answer to the nearest dollar.

Evaluate the integral .

Find the numerical value of by using the sum formulas.

Evaluate the integral .

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function.

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

Exam 13: A: Definite Integrals - Techniques

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

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place. ​

Use an integral formula to evaluate . ​

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

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11 ​

Use an integral formula to evaluate . ​

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

Suppose the Gini coefficient of income for a certain country is If the Lorenz curve for this country is , find the value of p. ​

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

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

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

Assume that the tax burden per capita (in dollars) for selected years from 1950 to 2002 can be modeled by where represents 1950. If the model remains valid, find the predicted average federal tax burden per capita from 2000 to 2010. Round your answer to the nearest dollar. ​

Evaluate the integral . ​

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

Evaluate the integral . ​

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles. ​

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function. ​

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

Find the numerical value of by using the sum formulas.

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

Use an integral formula to evaluate .

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

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11

Use an integral formula to evaluate .

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

Suppose the Gini coefficient of income for a certain country is If the Lorenz curve for this country is , find the value of p.

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

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

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

Assume that the tax burden per capita (in dollars) for selected years from 1950 to 2002 can be modeled by where represents 1950. If the model remains valid, find the predicted average federal tax burden per capita from 2000 to 2010. Round your answer to the nearest dollar.

Evaluate the integral .

Find the numerical value of by using the sum formulas.

Evaluate the integral .

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles.

If the marginal cost function for x units of a product is dollars per unit, and if the fixed cost is $120, find the total cost function.