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

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 3

Evaluate the integral   . ​

Accepted Answer

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

Question 4

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 24 to 92 units. Round your answer to the nearest penny. ​

Accepted Answer

A) $576.51 
B) $290.51 
C) $1,238.44 
D) $427.05 
E) $982.21 
A) $576.51 
B) $290.51 
C) $1,238.44 
D) $427.05 
E) $982.21

Question 5

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 6

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 7

For a certain product, the total revenue is given by   , and the total cost is given by   . Write an integral that gives the average profit for the product over the interval from 4 to 11 ​

Accepted Answer

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

Question 8

Consider the following supply and demand schedules, with p in dollars and x as the number of units.   Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables. ​

Accepted Answer

A) $6,466.67 
B) $23,333.33 
C) $16,166.67 
D) $26,366.67 
E) $13,133.33 
A) $6,466.67 
B) $23,333.33 
C) $16,166.67 
D) $26,366.67 
E) $13,133.33

Question 9

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 10

Find the area of the shaded region. ​
​

Accepted Answer

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

Question 11

Find the producer's surplus for a product with demand function   and supply function   where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

Accepted Answer

A) 37.5 million dollars 
B) 26.5 million dollars 
C) 21.0 million dollars 
D) 22.5 million dollars 
E) 23.5 million dollars 
A) 37.5 million dollars 
B) 26.5 million dollars 
C) 21.0 million dollars 
D) 22.5 million dollars 
E) 23.5 million dollars

Question 12

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function   where   represents 1985. Find the predicted total receipts for world tourism for the decade from 2011 to 2021. Round your answer to one decimal place. ​

Accepted Answer

A) $4,942.1 billion 
B) $17,546.4 billion 
C) $7,164.4 billion 
D) $10,754.3 billion 
E) $14,147.4 billion 
A) $4,942.1 billion 
B) $17,546.4 billion 
C) $7,164.4 billion 
D) $10,754.3 billion 
E) $14,147.4 billion

Question 13

For the interval [-2,10] and n = 4, find the values of   ​

Accepted Answer

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

Question 14

Evaluate   . ​

Accepted Answer

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

Question 15

Use the figure to decide which of   is larger, or if they are equal. ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 16

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function   . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Accepted Answer

A) 0.242 
B) 0.567 
C) 0.391 
D) 0.758 
E) 0.609 
A) 0.242 
B) 0.567 
C) 0.391 
D) 0.758 
E) 0.609

Question 17

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 18

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

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 19

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 20

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 2 to 7. Round your answer to the nearest cent. ​

Accepted Answer

A) $37,861.91 
B) $32,623.16 
C) $89,736.51 
D) $51,870.82 
E) $36,528.74 
A) $37,861.91 
B) $32,623.16 
C) $89,736.51 
D) $51,870.82 
E) $36,528.74

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

Use an integral formula to evaluate .

Evaluate the integral .

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 24 to 92 units. Round your answer to the nearest penny.

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

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.

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

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

Find the area of the shaded region.

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2011 to 2021. Round your answer to one decimal place.

For the interval [-2,10] and n = 4, find the values of

Evaluate .

Use the figure to decide which of is larger, or if they are equal.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Use an integral formula to evaluate .

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

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.

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 2 to 7. Round your answer to the nearest cent.

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Functions of Two or More Variables

Filters

Exam 14: Definite Integrals: Techniques of Integration

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

Use an integral formula to evaluate . ​

Evaluate the integral . ​

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 24 to 92 units. Round your answer to the nearest penny. ​

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

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. ​

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11 ​

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables. ​

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

Find the area of the shaded region. ​ ​

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place. ​

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2011 to 2021. Round your answer to one decimal place. ​

For the interval [-2,10] and n = 4, find the values of ​

Evaluate . ​

Use the figure to decide which of is larger, or if they are equal. ​

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​

Use an integral formula to evaluate . ​

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

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. ​

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 2 to 7. Round your answer to the nearest cent. ​

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Functions of Two or More Variables

Filters

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

Use an integral formula to evaluate .

Evaluate the integral .

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 24 to 92 units. Round your answer to the nearest penny.

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

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.

For a certain product, the total revenue is given by , and the total cost is given by . Write an integral that gives the average profit for the product over the interval from 4 to 11

Consider the following supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the producer's surplus at market equilibrium to 2 decimal places. Note that market equilibrium can be found from the tables.

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

Find the area of the shaded region.

Find the producer's surplus for a product with demand function and supply function where p is in millions of dollars and x is the number of thousands of units. Round your answer to one decimal place.

With data for 1990 to 2002, the total receipts for world tourism (in billions of dollars per year) can be modeled by the function where represents 1985. Find the predicted total receipts for world tourism for the decade from 2011 to 2021. Round your answer to one decimal place.

For the interval [-2,10] and n = 4, find the values of

Evaluate .

Use the figure to decide which of is larger, or if they are equal.

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.

Use an integral formula to evaluate .

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

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.

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 2 to 7. Round your answer to the nearest cent.