Question 1

Evaluate the integral   . ​

Accepted Answer

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

Question 2

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 3

If the supply function for x units of a commodity is   dollars, what is the producer's surplus at   ? Round your answer to the nearest dollar. ​

Accepted Answer

A)  $8,229 
B)  $1,969 
C)  $3,741 
D)  $1,559 
E)  $2,730 
A)  $8,229 
B)  $1,969 
C)  $3,741 
D)  $1,559 
E)  $2,730

Question 4

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 5

Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places.   where a = 300, b = 200, c = 400 ​

Accepted Answer

A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft 
A)  64,000 sq ft 
B)  106,666.67 sq ft 
C)  120,000 sq ft 
D)  58,666.67 sq ft 
E)  51,200 sq ft

Question 6

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

Accepted Answer

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

Question 7

Use integration by parts to evaluate the integral   ​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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 10

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 11

Evaluate   . ​

Accepted Answer

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

Question 12

Suppose the rate of production of a new line of products is given by   where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced. ​

Accepted Answer

A)  505 units 
B)  695 units 
C)  895 units 
D)  305 units 
E)  495 units 
A)  505 units 
B)  695 units 
C)  895 units 
D)  305 units 
E)  495 units

Question 13

A continuous income stream has an annual rate of flow at time t given by   (dollars per year). Find the present value of this income stream for the next 9 years, if the money is worth 4% compounded continuously. Round to the nearest dollar. ​

Accepted Answer

A)  $47,664 
B)  $107,767 
C)  $178,262 
D)  $147,471 
E)  $81,028 
A)  $47,664 
B)  $107,767 
C)  $178,262 
D)  $147,471 
E)  $81,028

Question 14

The demand function for a product is   , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places. ​

Accepted Answer

A)  $22.86 
B)  $28.24 
C)  $48.00 
D)  $62.40 
E)  $115.20 
A)  $22.86 
B)  $28.24 
C)  $48.00 
D)  $62.40 
E)  $115.20

Question 15

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 16

Find the average value of the function   over   ​

Accepted Answer

A)  48 
B)  96 
C)  44 
D)  12 
E)  -36 
A)  48 
B)  96 
C)  44 
D)  12 
E)  -36

Question 17

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 18

Suppose the marginal cost for x units of a good is   (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

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

Suppose the number of daily sales of a product was found to be given by   , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from   to   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  $133 
B)  $130 
C)  $127 
D)  $265 
E)  $255 
A)  $133 
B)  $130 
C)  $127 
D)  $265 
E)  $255

Evaluate the integral .

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar.

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

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

Use integration by parts to evaluate the integral

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

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

Evaluate the definite integral .

Evaluate .

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced.

A continuous income stream has an annual rate of flow at time t given by (dollars per year). Find the present value of this income stream for the next 9 years, if the money is worth 4% compounded continuously. Round to the nearest dollar.

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places.

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

Find the average value of the function over

Use integration by parts to evaluate .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

Evaluate the definite integral .

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar.

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

Evaluate the integral . ​

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar. ​

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

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

Use integration by parts to evaluate the integral ​

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

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

Evaluate the definite integral . ​

Evaluate . ​

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced. ​

A continuous income stream has an annual rate of flow at time t given by (dollars per year). Find the present value of this income stream for the next 9 years, if the money is worth 4% compounded continuously. Round to the nearest dollar. ​

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places. ​

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

Find the average value of the function over ​

Use integration by parts to evaluate . ​

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good? ​

Evaluate the definite integral . ​

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar. ​

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

Evaluate the integral .

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

If the supply function for x units of a commodity is dollars, what is the producer's surplus at ? Round your answer to the nearest dollar.

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

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

Use integration by parts to evaluate the integral

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

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

Evaluate the definite integral .

Evaluate .

Suppose the rate of production of a new line of products is given by where x is the number of items produced and t is the number of weeks the products have been in production. How many units were produced in the first 3 weeks? Round your answer to the nearest unit produced.

A continuous income stream has an annual rate of flow at time t given by (dollars per year). Find the present value of this income stream for the next 9 years, if the money is worth 4% compounded continuously. Round to the nearest dollar.

The demand function for a product is , where p is the number of dollars and x is the number of units. If the equilibrium quantity is $7, what is the consumer's surplus? Round your answer to two decimal places.

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

Find the average value of the function over

Use integration by parts to evaluate .

Suppose the marginal cost for x units of a good is (dollars per unit) and if the fixed cost is $200 find the total cost function of the good?

Evaluate the definite integral .

Suppose the number of daily sales of a product was found to be given by , x days after the start of an advertising campaign for this product. Find the average daily sales during the first 25 days of the campaign-that is, from to . Round your answer to the nearest dollar.