Question 1

Find the area of the region enclosed by the graphs of   and   . ​

Accepted Answer

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

Question 2

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 3

Find the area of the region bounded by   ​

Accepted Answer

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

Question 4

Use an integral formula to evaluate   .

Accepted Answer

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

Question 5

Find the area of the shaded region. ​
​

Accepted Answer

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

Question 6

A franchise models the profit from its store as a continuous income stream with a monthly rate of flow at time t given by   (dollars per month). When a new store opens, its manager is judged against the model, with special emphasis on the second half of the first year. Find the total profit for the second 6-month period   to   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  $61,831 
B)  $51,679 
C)  $40,973 
D)  $30,821 
E)  $46,232 
A)  $61,831 
B)  $51,679 
C)  $40,973 
D)  $30,821 
E)  $46,232

Question 7

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 8

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 9

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 10

If the supply function for a commodity is   where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus at   ? Round your answer to the nearest million dollars. ​

Accepted Answer

A)  1,890,953 million dollars 
B)  2,875,020 million dollars 
C)  1,790,850 million dollars 
D)  2,079,000 million dollars 
E)  1,890,000 million dollars 
A)  1,890,953 million dollars 
B)  2,875,020 million dollars 
C)  1,790,850 million dollars 
D)  2,079,000 million dollars 
E)  1,890,000 million dollars

Question 11

Suppose that the Carter Car Service franchise finds that the income generated by its stores can be modeled by assuming that the income is a continuous stream with a monthly rate of flow at time t given by   (dollars per month). Find the total income from a Carter Car Service store for years 3 through 5 of operation and round to the nearest penny. ​

Accepted Answer

A)  $973,587.71 
B)  $2,307,500.23 
C)  $1,059,312.41 
D)  $1,684,306.74 
E)  $1,186,131.50 
A)  $973,587.71 
B)  $2,307,500.23 
C)  $1,059,312.41 
D)  $1,684,306.74 
E)  $1,186,131.50

Question 12

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

Accepted Answer

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

Question 13

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 14

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. Group members measure across the algae growth (see the Figure) and obtain the following data (in feet).  
Use Simpson's Rule to approximate the area of the algae growth and round your answer to the nearest square foot.   ​

Accepted Answer

A)  1,110 sq ft 
B)  1,553 sq ft 
C)  2,641 sq ft 
D)  2,019 sq ft 
E)  3,573 sq ft 
A)  1,110 sq ft 
B)  1,553 sq ft 
C)  2,641 sq ft 
D)  2,019 sq ft 
E)  3,573 sq ft

Question 15

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 16

Evaluate the integral   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  integral diverges 
A)    
B)    
C)    
D)    
E)  integral diverges

Question 17

Find the area of the region bounded by   ​

Accepted Answer

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

Question 18

Evaluate the definite integral   . ​

Accepted Answer

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

Question 19

Evaluate the integral   . ​

Accepted Answer

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

Question 20

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)  ​
​​  
​

Find the area of the region enclosed by the graphs of and .

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

Find the area of the region bounded by

Use an integral formula to evaluate .

Find the area of the shaded region.

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

Find the numerical value of by using the sum formulas.

Use an integral formula to evaluate .

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus at ? Round your answer to the nearest million dollars.

For what value of a is a probability density function?

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

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

Evaluate the integral .

Find the area of the region bounded by

Evaluate the definite integral .

Evaluate the integral .

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

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Exam 13: A: Definite Integrals - Techniques

Find the area of the region enclosed by the graphs of and . ​

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

Find the area of the region bounded by ​

Use an integral formula to evaluate .

Find the area of the shaded region. ​ ​

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

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

Use an integral formula to evaluate . ​

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus at ? Round your answer to the nearest million dollars. ​

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

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

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

Evaluate the integral .

Find the area of the region bounded by ​

Evaluate the definite integral . ​

Evaluate the integral . ​

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 area of the region enclosed by the graphs of and .

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

Find the area of the region bounded by

Find the area of the shaded region.

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

Find the numerical value of by using the sum formulas.

Use an integral formula to evaluate .

If the supply function for a commodity is where p is in millions of dollars and x is the number of thousands of units. What is the producer's surplus at ? Round your answer to the nearest million dollars.

For what value of a is a probability density function?

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

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

Find the area of the region bounded by

Evaluate the definite integral .

Evaluate the integral .