Question 1

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 2

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 3

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 4

True or false. For the function   gives the area between the graph of   and the x-axis from   .
​

Accepted Answer

A) True 
 B)False

Question 5

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 6

The demand function for a product is   where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars. ​

Accepted Answer

A)  114 million dollars 
B)  149 million dollars 
C)  83 million dollars 
D)  88 million dollars 
E)  174 million dollars 
A)  114 million dollars 
B)  149 million dollars 
C)  83 million dollars 
D)  88 million dollars 
E)  174 million dollars

Question 7

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 8

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 9

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

Accepted Answer

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

Question 10

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 11

The following income distribution data define points on Lorenz curves, where x represents the fraction of a certain country's population and L(x) the cumulative percent of income held by fraction x. Use this data and a numerical method to evaluate   and hence to find the Gini coefficient of income for this country in 1995 and 2003. Round your answers to three decimal places.  
​

Accepted Answer

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

Question 12

Suppose the marginal cost for x units of a good is   (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar. ​

Accepted Answer

A)  168 dollars 
B)  226 dollars 
C)  228 dollars 
D)  170 dollars 
E)  240 dollars 
A)  168 dollars 
B)  226 dollars 
C)  228 dollars 
D)  170 dollars 
E)  240 dollars

Question 13

The following income distribution data define points on Lorenz curves, where x represents the fraction of a certain country's population and L(x) the cumulative percent of income held by fraction x. Use this data and a numerical method to evaluate   and hence to find the Gini coefficient of income for this country in 1995 and 2003. Round your answers to three decimal places.

Accepted Answer

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

Question 14

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 15

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 16

For what value of c is the function   a probability density function? ​

Accepted Answer

A)  2,000 
B)  1,000 
C)  4,000 
D)  40,000 
E)  20,000 
A)  2,000 
B)  1,000 
C)  4,000 
D)  40,000 
E)  20,000

Question 17

Suppose that the rate of production of a product (in units per week) is measured at the end of each of the first 5 weeks after start-up, and the following data are obtained. Use the Trapezoidal Rule to approximate the total number of units produced in the first 5 weeks. Round your answer to two decimal places.

Accepted Answer

A)  1,323.15 units 
B)  2100.30 units 
C)  573.83 units 
D)  1667.90 units 
E)  833.60 units 
A)  1,323.15 units 
B)  2100.30 units 
C)  573.83 units 
D)  1667.90 units 
E)  833.60 units

Question 18

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 19

When the area under   from   to   is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​
Left-hand endpoints:   ​
Right-hand endpoints:   ​
Find   ​

Accepted Answer

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

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

Use integration by parts to evaluate .

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

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

True or false. For the function gives the area between the graph of and the x-axis from .

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).

The demand function for a product is where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars.

Find the numerical value of by using the sum formulas.

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.

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

Use an integral formula to evaluate .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar.

Evaluate the given integral with the Fundamental Theorem of Calculus .

Use an integral formula to evaluate .

For what value of c is the function a probability density function?

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.

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find

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Quadratic and Other Special Functions

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Inequalities and Linear Programming

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Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

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Derivatives Continued

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A: Definite Integrals - Techniques

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Exam 13: Definite Integrals - Techniques

Use integration by parts to evaluate . ​

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

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

True or false. For the function gives the area between the graph of and the x-axis from . ​

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). ​

The demand function for a product is where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars. ​

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

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. ​

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

Use an integral formula to evaluate . ​

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar. ​

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

Use an integral formula to evaluate . ​

For what value of c is the function a probability density function? ​

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. ​

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: ​ Left-hand endpoints: ​ Right-hand endpoints: ​ Find ​

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

Use integration by parts to evaluate .

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

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

True or false. For the function gives the area between the graph of and the x-axis from .

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).

The demand function for a product is where p is in millions of dollars and x is the number of thousands of units. If the equilibrium price is $6 million, what is the consumer's surplus? Round your answer to the nearest million dollars.

Find the numerical value of by using the sum formulas.

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.

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

Use an integral formula to evaluate .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200. What is the total cost of producing 4 units of this good? Round your answer to the nearest dollar.

Evaluate the given integral with the Fundamental Theorem of Calculus .

Use an integral formula to evaluate .

For what value of c is the function a probability density function?

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.

When the area under from to is approximated, the formulas for the sum of n rectangles using left-hand endpoints and right-hand endpoints are: Left-hand endpoints: Right-hand endpoints: Find