Question 1

Find the value of the given sum and round to four decimal places. ​   ​

Accepted Answer

A)  3.2405 
B)  2.3000 
C)  2.5571 
D)  2.0000 
E)  2.6250 
A)  3.2405 
B)  2.3000 
C)  2.5571 
D)  2.0000 
E)  2.6250

Question 2

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 3

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   and   .
​

Accepted Answer

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

Question 4

Use the Trapezoidal Rule to approximate   with n = 4. Round your answer to 3 decimal places. ​

Accepted Answer

A)  15.377 
B)  4.696 
C)  5.985 
D)  3.200 
E)  7.689 
A)  15.377 
B)  4.696 
C)  5.985 
D)  3.200 
E)  7.689

Question 5

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 6

Use Simpson's Rule to approximate   with n = 4. Round your answer to 2 decimal places. ​

Accepted Answer

A)  5.10 
B)  10.27 
C)  28.17 
D)  5.14 
E)  25.96 
A)  5.10 
B)  10.27 
C)  28.17 
D)  5.14 
E)  25.96

Question 7

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 8

The graph in the following figure gives the times that it takes a vehicle to reach speeds from 0 mph to 25 mph, in increments of 5 mph, with a curve connecting them. Count the squares under the curve to estimate this distance. Estimate the distance traveled by the vehicle in 14 seconds, to a speed of 25 mph. (Be careful with time units.)

Accepted Answer

A)  1/16 mile 
B)  4/15 mile 
C)  1/13 mile 
D)  1/9 mile 
E)  1/8 mile 
A)  1/16 mile 
B)  4/15 mile 
C)  1/13 mile 
D)  1/9 mile 
E)  1/8 mile

Question 9

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 10

Evaluate the definite integral   . ​

Accepted Answer

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

Question 11

The following table shows the rate of oil consumption (in thousands of barrels per year) by a certain city. Estimate the total consumption of oil by the city from 1999 -2004 by using 5 equal subdivisions and left-hand endpoints to estimate the area under the graph that corresponds to the table from 1999 to 2004.

Accepted Answer

A)  17.704 thousand barrels 
B)  16.632 thousand barrels 
C)  16.816 thousand barrels 
D)  17.546 thousand barrels 
E)  15.689 thousand barrels 
A)  17.704 thousand barrels 
B)  16.632 thousand barrels 
C)  16.816 thousand barrels 
D)  17.546 thousand barrels 
E)  15.689 thousand barrels

Question 12

Find the area, if it exists, of the region under the graph of   and to the right of   .

Accepted Answer

A)    
B)    
C)    
D)    
E)  does not exist 
A)    
B)    
C)    
D)    
E)  does not exist

Question 13

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 14

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 15

The demand function for a certain product is given by   , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​

Accepted Answer

A)  $834.16 
B)  $420.34 
C)  $1,791.90 
D)  $617.90 
E)  $1,421.16 
A)  $834.16 
B)  $420.34 
C)  $1,791.90 
D)  $617.90 
E)  $1,421.16

Question 16

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 17

Use integration by parts to evaluate the integral   ​

Accepted Answer

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

Question 18

Find the area of the shaded region. ​
​

Accepted Answer

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

Question 19

Evaluate   . ​

Accepted Answer

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

Question 20

The demand function for a certain product is   and the supply function is   where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

Accepted Answer

A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars 
A)  Equilibrium point: (4, 64); Consumer's surplus: 43 million dollars 
B)  Equilibrium point: (10, 64); Consumer's surplus: 123 million dollars 
C)  Equilibrium point: (8, 64); Consumer's surplus: 203 million dollars 
D)  Equilibrium point: (4, 8); Consumer's surplus: 187 million dollars 
E)  Equilibrium point: (10, 8); Consumer's surplus: 107 million dollars

Find the value of the given sum and round to four decimal places.

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.

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 and .

Use the Trapezoidal Rule to approximate with n = 4. Round your answer to 3 decimal places.

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 Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places.

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

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

Evaluate the definite integral .

Find the area, if it exists, of the region under the graph of and to the right of .

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 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.

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.

Use integration by parts to evaluate .

Use integration by parts to evaluate the integral

Find the area of the shaded region.

Evaluate .

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.

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 value of the given sum and round to four decimal places. ​ ​

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. ​

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 and . ​

Use the Trapezoidal Rule to approximate with n = 4. Round your answer to 3 decimal places. ​

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 Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places. ​

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

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

Evaluate the definite integral . ​

Find the area, if it exists, of the region under the graph of and to the right of .

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 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. ​

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny. ​

Use integration by parts to evaluate . ​

Use integration by parts to evaluate the integral ​

Find the area of the shaded region. ​ ​

Evaluate . ​

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable. ​

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 value of the given sum and round to four decimal places.

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.

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 and .

Use the Trapezoidal Rule to approximate with n = 4. Round your answer to 3 decimal places.

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 Simpson's Rule to approximate with n = 4. Round your answer to 2 decimal places.

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

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

Evaluate the definite integral .

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 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.

The demand function for a certain product is given by , where p is the price and q is the number of units demanded. Find the average price as demand ranges from 35 to 81 units. Round your answer to the nearest penny.

Use integration by parts to evaluate .

Use integration by parts to evaluate the integral

Find the area of the shaded region.

Evaluate .

The demand function for a certain product is and the supply function is where p is in millions of dollars and x is the number of thousands of units. Find the equilibrium point (x, p) and the consumer's surplus there. Round your answer to the nearest million dollars, where applicable.