Question 1

Evaluate the integral   .

Accepted Answer

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

Question 2

The total cost function for a product is   , and the demand function is   , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Accepted Answer

A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86 
A)  $256.00 
B)  $295.38 
C)  $576.00 
D)  $384.00 
E)  $182.86

Question 3

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 4

Evaluate the integral   . ​

Accepted Answer

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

Question 5

Evaluate the integral   . ​
​

Accepted Answer

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

Question 6

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 7

Use the sum formulas to find the value of the sum that follows. ​   ​

Accepted Answer

A)  720 
B)  160 
C)  435 
D)  820 
E)  90 
A)  720 
B)  160 
C)  435 
D)  820 
E)  90

Question 8

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 9

Use the function   from   to   and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find   by using the formula for the sum of the areas of the n rectangles. ​

Accepted Answer

A)  10 
B)  30 
C)  60 
D)  12 
E)  14 
A)  10 
B)  30 
C)  60 
D)  12 
E)  14

Question 10

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

Accepted Answer

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

Question 11

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 12

Use the sum formulas to find the value of the sum that follows. ​   ​

Accepted Answer

A)  720 
B)  160 
C)  435 
D)  820 
E)  90 
A)  720 
B)  160 
C)  435 
D)  820 
E)  90

Question 13

Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by   in thousands of dollars per year. Find the total income from the machines predicted by the model over the first 5 years. Round your answer to the nearest thousand dollars. ​

Accepted Answer

A)  $29,743,000 
B)  $592,000 
C)  $743,000 
D)  $897,000 
E)  $29,592,000 
A)  $29,743,000 
B)  $592,000 
C)  $743,000 
D)  $897,000 
E)  $29,592,000

Question 14

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars. ​​

Accepted Answer

A)  ​270 million dollars 
B)  ​267 million dollars 
C)  ​257 million dollars 
D)  ​181 million dollars 
E)  ​219 million dollars 
A)  ​270 million dollars 
B)  ​267 million dollars 
C)  ​257 million dollars 
D)  ​181 million dollars 
E)  ​219 million dollars

Question 15

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 16

The average life for a particular brand of car battery is given by the following probability density function where t is in years.   ​Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places. ​

Accepted Answer

A)  1.72 
B)  0.43 
C)  0.54 
D)  0.34 
E)  0.65 
A)  1.72 
B)  0.43 
C)  0.54 
D)  0.34 
E)  0.65

Question 17

Evaluate the integral   . ​

Accepted Answer

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

Question 18

Evaluate the integral   . ​

Accepted Answer

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

Question 19

The cost of producing x units of a certain item is   Find the average value of the cost function C(x) over the interval from 0 to 1,000. Round answer to nearest penny. ​

Accepted Answer

A)  $933,866.67 
B)  $2,801,600.00 
C)  $549,333.33 
D)  $3,735,466.67 
E)  $2,147,893.33 
A)  $933,866.67 
B)  $2,801,600.00 
C)  $549,333.33 
D)  $3,735,466.67 
E)  $2,147,893.33

Question 20

Use Simpson's Rule to approximate   with n = 4. Round your answer to 3 decimal places. ​

Accepted Answer

A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123 
A)  0.562 
B)  0.066 
C)  1.617 
D)  0.733 
E)  2.123

Evaluate the integral .

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Evaluate the integral .

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.

Use the sum formulas to find the value of the sum that follows.

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles.

Find the numerical value of by using the sum formulas.

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 the sum formulas to find the value of the sum that follows.

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars.

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

The average life for a particular brand of car battery is given by the following probability density function where t is in years. Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places.

Evaluate the integral .

Evaluate the integral .

The cost of producing x units of a certain item is Find the average value of the cost function C(x) over the interval from 0 to 1,000. Round answer to nearest penny.

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.

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

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Algebraic Concepts 3

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Exam 13: Definite Integrals - Techniques

Evaluate the integral .

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent. ​

Evaluate the integral . ​

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.

Use the sum formulas to find the value of the sum that follows. ​ ​

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles. ​

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

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 the sum formulas to find the value of the sum that follows. ​ ​

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars. ​​

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

The average life for a particular brand of car battery is given by the following probability density function where t is in years. ​Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places. ​

Evaluate the integral . ​

Evaluate the integral . ​

The cost of producing x units of a certain item is Find the average value of the cost function C(x) over the interval from 0 to 1,000. Round answer to nearest penny. ​

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places. ​

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

The total cost function for a product is , and the demand function is , where p is the number of dollars and x is the number of units. Find the consumer's surplus at the point where the product has maximum profit. Round to the nearest cent.

Evaluate the integral .

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.

Use the sum formulas to find the value of the sum that follows.

Use the function from to and n equal subintervals with the function evaluated at the right-hand endpoints of each subinterval. Let the sum of the areas of the rectangles be S. Find by using the formula for the sum of the areas of the n rectangles.

Find the numerical value of by using the sum formulas.

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 the sum formulas to find the value of the sum that follows.

If the demand function for a 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 consumer's surplus. Round your answer to the nearest million dollars.

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

The average life for a particular brand of car battery is given by the following probability density function where t is in years. Find the probability that a battery chosen at random lasts between 2 and 7 years. Round your answer to two decimal places.

Evaluate the integral .

Evaluate the integral .

The cost of producing x units of a certain item is Find the average value of the cost function C(x) over the interval from 0 to 1,000. Round answer to nearest penny.

Use Simpson's Rule to approximate with n = 4. Round your answer to 3 decimal places.