Question 1

Use integration by parts to evaluate the integral   ​

Accepted Answer

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

Question 2

Evaluate the definite integral   . ​

Accepted Answer

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

Question 3

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)    B

Question 4

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 5

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

Accepted Answer

A)  1 
B)  0 
C)  ​   
D)    
E)  diverges 
A)  1 
B)  0 
C)  ​   
D)    
E)  diverges

Question 6

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Accepted Answer

A)    
B)  2 
C)  4 
D)    
E)  3 
A)    
B)  2 
C)  4 
D)    
E)  3

Question 7

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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 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 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 12

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​
I. Integration by parts 
II  
III.  
IV.  
  ​

Accepted Answer

A)  I. Integration by parts; 
  
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied 
A)  I. Integration by parts; 
  
B)    
C)    
D)  ​   
E)  not integrable by any of the techniques we have studied

Question 13

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 14

Find the value of the sum   ​

Accepted Answer

A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622 
A)  8,784 
B)  8,808 
C)  5,675 
D)  8,800 
E)  2,622

Question 15

The total cost function for a product is   , and the demand function is   , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Accepted Answer

A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86 
A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86

Question 16

Use the figure to decide which of   is larger, or if they are equal. ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 17

Evaluate   . ​

Accepted Answer

A)  8 
B)  2 
C)  6 
D)  3 
E)  0 
A)  8 
B)  2 
C)  6 
D)  3 
E)  0

Question 18

The United States' spending for military (in billions of dollars per year) can be modeled by   , where   represents 1993. Estimate the total spending for the United States military between 2000 and 2005 by using 10 equal subdivisions and right-hand endpoints to approximate the area under the graph of M(t) between   and   . Round to three decimal places. ​

Accepted Answer

A)  3,018.8 billion dollars 
B)  2,709.062 billion dollars 
C)  2,735.034 billion dollars 
D)  2,473.582 billion dollars 
E)  2,785.842 billion dollars 
A)  3,018.8 billion dollars 
B)  2,709.062 billion dollars 
C)  2,735.034 billion dollars 
D)  2,473.582 billion dollars 
E)  2,785.842 billion dollars

Question 19

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 20

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

Use integration by parts to evaluate the integral

Evaluate the definite integral .

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

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

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

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Use an integral formula to evaluate .

For what value of a is a probability density function?

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

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

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.

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II III. IV.

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

Find the value of the sum

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Use the figure to decide which of is larger, or if they are equal.

Evaluate .

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

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

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Algebraic Concepts 2

Algebraic Concepts 3

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Exam 13: Definite Integrals - Techniques

Use integration by parts to evaluate the integral ​

Evaluate the definite integral . ​

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 ​

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

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

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Use an integral formula to evaluate . ​

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

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

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

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. ​

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. ​ I. Integration by parts II III. IV. ​

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

Find the value of the sum ​

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Use the figure to decide which of is larger, or if they are equal. ​

Evaluate . ​

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

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 the integral

Evaluate the definite integral .

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

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

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

Use an integral formula to evaluate .

For what value of a is a probability density function?

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

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

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.

Determine the most appropriate method or integral formula for evaluating the given integral. Next, evaluate the integral. I. Integration by parts II III. IV.

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

Find the value of the sum

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Use the figure to decide which of is larger, or if they are equal.

Evaluate .

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