Question 1

Evaluate the definite integral   . ​

Accepted Answer

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

Question 2

Suppose that the demand for q units of a certain product at p per unit is given by   . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.​ ​

Accepted Answer

A)  $851.85 
B)  $426.11 
C)  $1,032.79 
D)  $2,365.69 
E)  $4,259.26 
A)  $851.85 
B)  $426.11 
C)  $1,032.79 
D)  $2,365.69 
E)  $4,259.26

Question 3

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 4

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

Accepted Answer

A)  49.11 
B)  98.00 
C)  261.78 
D)  86.89 
E)  260.00 
A)  49.11 
B)  98.00 
C)  261.78 
D)  86.89 
E)  260.00

Question 5

Find the average value of the given function over the given interval. ​

Accepted Answer

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

Question 6

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 7

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Accepted Answer

A)    
B)  2 
C)  4 
D)    
E)  3 
A)    
B)  2 
C)  4 
D)    
E)  3

Question 8

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 9

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

Accepted Answer

A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493 
A)  $33,846 
B)  $27,060 
C)  $29,927 
D)  $13,420 
E)  $31,493

Question 10

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 11

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 12

Evaluate the definite integral   . ​

Accepted Answer

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

Question 13

Evaluate the integral   .

Accepted Answer

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

Question 14

A franchise models the profit from its store as a continuous income stream with a monthly rate of flow at time t given by   (dollars per month). When a new store opens, its manager is judged against the model, with special emphasis on the second half of the first year. Find the total profit for the second 6-month period   to   . Round your answer to the nearest dollar. ​

Accepted Answer

A)  $61,831 
B)  $51,679 
C)  $40,973 
D)  $30,821 
E)  $46,232 
A)  $61,831 
B)  $51,679 
C)  $40,973 
D)  $30,821 
E)  $46,232

Question 15

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 16

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 17

Use an integral formula to evaluate   . ​

Accepted Answer

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

Question 18

Use integration by parts to evaluate   . ​

Accepted Answer

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

Question 19

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 20

For the interval [-5,2] and for n = 3 find h.

Accepted Answer

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

Evaluate the definite integral .

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.

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.

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

Find the average value of the given function over the given interval.

Use an integral formula to evaluate .

Find the area of the shaded region. Round to the nearest hundredth if necessary.

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Use an integral formula to evaluate .

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.

Evaluate the definite integral .

Evaluate the integral .

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.

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.

Use an integral formula to evaluate .

Use integration by parts to evaluate .

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.

For the interval [-5,2] and for n = 3 find h.

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

Exam 13: A: Definite Integrals - Techniques

Evaluate the definite integral . ​

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.​ ​

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. ​

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

Find the average value of the given function over the given interval. ​

Use an integral formula to evaluate . ​

Find the area of the shaded region. Round to the nearest hundredth if necessary.

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

Use an integral formula to evaluate . ​

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. ​

Evaluate the definite integral . ​

Evaluate the integral .

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. ​

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. ​

Use an integral formula to evaluate . ​

Use integration by parts to evaluate . ​

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. ​

For the interval [-5,2] and for n = 3 find h.

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 definite integral .

Suppose that the demand for q units of a certain product at p per unit is given by . Use Simpson's Rule with n = 6 to approximate the average price as demand ranges from 3 to 8 items to the nearest cent.

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.

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

Find the average value of the given function over the given interval.

Use an integral formula to evaluate .

Suppose the following table gives the supply and demand schedules, with p in dollars and x as the number of units. Use Simpson's Rule to approximate the consumer's surplus at market equilibrium. Note that market equilibrium can be found from the tables.

Use an integral formula to evaluate .

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.

Evaluate the definite integral .

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.

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.

Use an integral formula to evaluate .

Use integration by parts to evaluate .

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.