Question 1

Evaluate the definite integral   . ​

Accepted Answer

A)  0 
B)  1125 
C)  -1125 
D)  -2250 
E)  2250 
A)  0 
B)  1125 
C)  -1125 
D)  -2250 
E)  2250

Question 2

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 3

Find the average value of the function   ​

Accepted Answer

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

Question 4

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 5

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​   ​

Accepted Answer

A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist 
A)  49 
B)  50 
C)  8 
D)  7 
E)  does not exist

Question 6

Find the value of the sum   , if   . ​

Accepted Answer

A)  64 
B)  60 
C)  20 
D)  8 
E)  32 
A)  64 
B)  60 
C)  20 
D)  8 
E)  32

Question 7

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 8

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by   where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​

Accepted Answer

A)  120 years 
B)  137 years 
C)  84 years 
D)  270 years 
E)  47 years 
A)  120 years 
B)  137 years 
C)  84 years 
D)  270 years 
E)  47 years

Question 9

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 10

Use the table values and apply the Simpson's Rule to approximate   to one decimal place.

Accepted Answer

A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3 
A)  1.7 
B)  1.6 
C)  1.3 
D)  2.0 
E)  2.3

Evaluate the definite integral .

Find the average value of the function

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

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Find the value of the sum , if .

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.

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year.

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

Use the table values and apply the Simpson's Rule to approximate 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

Exam 13: Definite Integrals - Techniques

Evaluate the definite integral . ​

Find the average value of the function ​

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

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​ ​

Find the value of the sum , if . ​

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. ​

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year. ​

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

Use the table values and apply the Simpson's Rule to approximate 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

Evaluate the definite integral .

Find the average value of the function

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

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Find the value of the sum , if .

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.

With the data for selected years from 1920 to 2007, the life span of individuals in a country can be modeled by where x = 0 represents 1900. Find the predicted average life span from 2040 to 2055. Round your answer to the nearest year.

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