Question 1

Evaluate the definite integral   . ​

Accepted Answer

A)  -160 
B)  -290 
C)  -70 
D)  -140 
E)  -65 
A)  -160 
B)  -290 
C)  -70 
D)  -140 
E)  -65

Question 2

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function   . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places. ​

Accepted Answer

A)  0.865 
B)  0.998 
C)  0.145 
D)  0.135 
E)  0.002 
A)  0.865 
B)  0.998 
C)  0.145 
D)  0.135 
E)  0.002

Question 5

Evaluate the definite integral   . ​

Accepted Answer

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

Question 6

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 7

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by   in thousands of dollars per year. Find the total income over the next 20 years. ​

Accepted Answer

A)    thousand dollars 
B)    thousand dollars 
C)    thousand dollars 
D)    thousand dollars 
E)    thousand dollars 
A)    thousand dollars 
B)    thousand dollars 
C)    thousand dollars 
D)    thousand dollars 
E)    thousand dollars

Question 8

Use the table of values to approximate   Use Simpson's Rule and round your answers to one decimal place. ​
 
​

Accepted Answer

A)  82.2 
B)  41.1 
C)  27.4 
D)  13.7 
E)  4.6 
A)  82.2 
B)  41.1 
C)  27.4 
D)  13.7 
E)  4.6

Question 9

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 10

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 11

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 12

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

Accepted Answer

A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84 
A)  $3,576.9 
B)  $2,928.14 
C)  $25,657.84 
D)  $3,056.14 
E)  $25,785.84

Question 13

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 14

Evaluate the integral   .

Accepted Answer

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

Question 15

Suppose that the output of the machinery in a factory can be considered as a continuous income stream with an annual rate of flow at time t given by   in thousands of dollars per year. If the annual interest rate is 4% compounded continuously, find the capital value of the machinery. Round your answer to the nearest dollar. ​

Accepted Answer

A)  $4,406,250 
B)  $1,175,000 
C)  $1,958,333 
D)  $6,462,500 
E)  $2,937,500 
A)  $4,406,250 
B)  $1,175,000 
C)  $1,958,333 
D)  $6,462,500 
E)  $2,937,500

Question 16

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 17

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by   (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent. ​

Accepted Answer

A)  $165,371.54 
B)  $142,489.95 
C)  $391,947.09 
D)  $226,559.01 
E)  $159,548.60 
A)  $165,371.54 
B)  $142,489.95 
C)  $391,947.09 
D)  $226,559.01 
E)  $159,548.60

Question 18

If the demand function for wheat is   dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at   Round answer to the nearest cent. ​

Accepted Answer

A)  $839.61 
B)  $1297.58 
C)  $1679.22 
D)  $1903.12 
E)  $2854.68 
A)  $839.61 
B)  $1297.58 
C)  $1679.22 
D)  $1903.12 
E)  $2854.68

Question 19

For what value of a is   a probability density function? ​

Accepted Answer

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

Question 20

Suppose the presence of phosphates in certain waste products dumped into a lake promotes the growth of algae. Rampant growth of algae affects the oxygen supply in the water, so an environmental group wishes to estimate the area of algae growth. The group measures the length across the algae growth (see the figure) and obtains the following data (in feet).  
Use 8 rectangles with bases of 10 feet and lengths measured at the left-hand endpoints to approximate the area of the algae growth.   ​
​

Accepted Answer

A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft 
A)  1,730 sq ft 
B)  1,704 sq ft 
C)  2,076 sq ft 
D)  2,520 sq ft 
E)  2,556 sq ft

Evaluate the definite integral .

Use an integral formula to evaluate .

Find the area of the region enclosed by and .

In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places.

Evaluate the definite integral .

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

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years.

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

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.

Use integration by parts to evaluate .

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

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

Find the average value of the function over

Evaluate the integral .

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

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent.

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent.

For what value of a is a probability density function?

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

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Algebraic Concepts 5

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Exam 13: Definite Integrals - Techniques

Evaluate the definite integral . ​

Use an integral formula to evaluate . ​

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

In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places. ​

Evaluate the definite integral . ​

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

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years. ​

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place. ​ ​

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. ​

Use integration by parts to evaluate . ​

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 ​

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

Find the average value of the function over ​

Evaluate the integral .

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

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent. ​

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent. ​

For what value of a is a probability density function? ​

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 .

Use an integral formula to evaluate .

Find the area of the region enclosed by and .

In a manufacturing process involving several machines, the average down time t (in hours) for a machine that needs repair has the probability density function . Find the probability that a failed machine's down time is 4 hours or more. Round your answer to three decimal places.

Evaluate the definite integral .

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

Suppose the income from an Internet access business is a continuous income stream with annual rate of flow given by in thousands of dollars per year. Find the total income over the next 20 years.

Use the table of values to approximate Use Simpson's Rule and round your answers to one decimal place.

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.

Use integration by parts to evaluate .

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

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

Find the average value of the function over

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

The Carter Car Service franchise has a continuous income stream with a monthly rate of flow modeled by (dollars per month). Find the average flow of income over years 4 to 5. Round your answer to the nearest cent.

If the demand function for wheat is dollars, where x is the number of hundreds of bushels of wheat, estimate the consumer's surplus at Round answer to the nearest cent.

For what value of a is a probability density function?