Question 1

Use Simpson's Rule to approximate   with n = 6. Round your answer to 3 decimal places. ​

Accepted Answer

A)  3.325 
B)  1.650 
C)  8.808 
D)  1.869 
E)  9.030 
A)  3.325 
B)  1.650 
C)  8.808 
D)  1.869 
E)  9.030

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 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 4

Suppose that a printing firm considers the production of its presses as a continuous income stream. If the annual rate of flow at time t is given by   in thousands of dollars per year, and if money is worth 7% compounded continuously, find the present value and future value of the presses over the next 10 years. Round your answer to the nearest dollar. ​

Accepted Answer

A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424 
A)  Present Value: $212,562; Future Value: $428,047 
B)  Present Value: $181,071; Future Value: $364,632 
C)  Present Value: $119,242; Future Value: $240,124 
D)  Present Value: $193,878; Future Value: $390,422 
E)  Present Value: $127,833; Future Value: $257,424

Question 5

A 58-year-old couple are considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Video Rental Palace. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by   (dollars per year) and the Video Palace has a continuous income stream with a projected annual rate of flow at time t given by   (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Determine which is the better buy by finding the present value of each business over the next 6 years (until the couple reach age 64). ​

Accepted Answer

A)  the Video Palace 
B)  the Gift Shoppe 
A)  the Video Palace 
B)  the Gift Shoppe

Question 6

Evaluate the integral   .

Accepted Answer

A)  0 
B)    
C)    
D)    
E)  integral diverges 
A)  0 
B)    
C)    
D)    
E)  integral diverges

Question 7

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.   ​ ​

Accepted Answer

A)  1.905 
B)  2.858 
C)  4.858 
D)  8.001 
E)  9.716 
A)  1.905 
B)  2.858 
C)  4.858 
D)  8.001 
E)  9.716

Question 8

Use an integral formula to evaluate   . ​

Accepted Answer

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

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 the function   from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-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 11

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 12

Evaluate   . ​

Accepted Answer

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

Question 13

The demand function for a product is   , and the supply function for it is   , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

Accepted Answer

A)  $34.51 
B)  $58.67 
C)  $152.53 
D)  $82.13 
E)  $176.00 
A)  $34.51 
B)  $58.67 
C)  $152.53 
D)  $82.13 
E)  $176.00

Question 14

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 15

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 16

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 17

Use the Trapezoidal Rule to approximate   with n = 6. Round your answer to two decimal places. ​

Accepted Answer

A)  1091.56 
B)  323.56 
C)  545.78 
D)  212.44 
E)  444.44 
A)  1091.56 
B)  323.56 
C)  545.78 
D)  212.44 
E)  444.44

Question 18

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 19

Evaluate the definite integral   . ​

Accepted Answer

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

Question 20

The rate of depreciation of a building is given by   dollars per year,   . Use the definite integral to find the total depreciation over the first 20 years. ​

Accepted Answer

A)  $700,000 
B)  $35,000 
C)  ​$350,000 
D)  $200,000 
E)  $1,400,000 
A)  $700,000 
B)  $35,000 
C)  ​$350,000 
D)  $200,000 
E)  $1,400,000

Use Simpson's Rule to approximate with n = 6. Round your answer to 3 decimal places.

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

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).

Evaluate the integral .

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.

Use an integral formula to evaluate .

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

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

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

Evaluate .

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

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

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

Find the value of the sum , if .

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Use an integral formula to evaluate .

Evaluate the definite integral .

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years.

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

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Exam 13: A: Definite Integrals - Techniques

Use Simpson's Rule to approximate with n = 6. Round your answer to 3 decimal places. ​

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

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). ​

Evaluate the integral .

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places. ​ ​

Use an integral formula to evaluate . ​

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

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S). ​

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

Evaluate . ​

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent. ​

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

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 ​

Find the value of the sum , if . ​

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places. ​

Use an integral formula to evaluate . ​

Evaluate the definite integral . ​

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years. ​

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

Use Simpson's Rule to approximate with n = 6. Round your answer to 3 decimal places.

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

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).

Use formulas or numerical integration with a graphing calculator or computer to evaluate the given definite integral. Round answer to three decimal places.

Use an integral formula to evaluate .

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

Use the function from x = 0 to x = 1 and n equal subintervals with the function evaluated at the left-hand endpoints of each subinterval. Find a formula for the sum of the areas of the n rectangles (call this S).

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

Evaluate .

The demand function for a product is , and the supply function for it is , where p is the number of dollars and x is the number of units. If the equilibrium price is $248 what is the producer's surplus at the equilibrium price? Round to the nearest cent.

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

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

Find the value of the sum , if .

Use the Trapezoidal Rule to approximate with n = 6. Round your answer to two decimal places.

Use an integral formula to evaluate .

Evaluate the definite integral .

The rate of depreciation of a building is given by dollars per year, . Use the definite integral to find the total depreciation over the first 20 years.