Question 1

​Approximate the definite integral "by hand," using the Trapezoidal Rule with   trapezoids.Round answer to three decimal places.   ​

Accepted Answer

A)  ​13.716 
B)  ​23.708 
C)  ​11.854 
D)  ​17.145 
E)  ​18.966 
A)  ​13.716 
B)  ​23.708 
C)  ​11.854 
D)  ​17.145 
E)  ​18.966

Question 2

​The probability of recall in an experiment is modeled by   ,   where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places. ​

Accepted Answer

A)  ​0.387 
B)  ​0.221 
C)  ​0.685 
D)  ​0.173 
E)  ​0.867 
A)  ​0.387 
B)  ​0.221 
C)  ​0.685 
D)  ​0.173 
E)  ​0.867

Question 3

​Approximate the integral using Simpson's Rule:   ,   Round your answer to three decimal places. ​

Accepted Answer

A)  ​0.85 
B)  ​1.017 
C)  ​1.284 
D)  ​1.161 
E)  ​0.652 
A)  ​0.85 
B)  ​1.017 
C)  ​1.284 
D)  ​1.161 
E)  ​0.652

Question 4

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 5

Use the error formulas to find ​n such that the error in the approximation of the definite integral   is less than 0.0001 using the Trapezoidal Rule. ​

Accepted Answer

A)  ​77 
B)  ​78 
C)  ​76 
D)  ​74 
E)  ​75 
A)  ​77 
B)  ​78 
C)  ​76 
D)  ​74 
E)  ​75

Question 6

​Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. ​   ​

Accepted Answer

A)  ​converges to 0 
B)  converges to 5 
C)  ​converges to   
D)  ​diverges to   
E)  ​​diverges to   
A)  ​converges to 0 
B)  converges to 5 
C)  ​converges to   
D)  ​diverges to   
E)  ​​diverges to

Question 7

Find the definite integral. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 8

Use integration by parts to find the integral below. ​   ,(   ,   )
​

Accepted Answer

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

Question 9

​Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ​   ,   ​

Accepted Answer

A)  ​$210,000 
B)  ​​$200,000 
C)  ​​$220,000 
D)  ​​$240,000 
E)  ​​$230,000 
A)  ​$210,000 
B)  ​​$200,000 
C)  ​​$220,000 
D)  ​​$240,000 
E)  ​​$230,000

Question 10

The rate of change in the number of subscribers S to a newly introduced magazine is modeled by   ,   where t is the time in years.Use Simpson's Rule with   to estimate the total increase in the number of subscribers during the first 6 years. ​

Accepted Answer

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

Question 11

Identify u and dv for finding the integral using integration by parts.   ​

Accepted Answer

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

Question 12

Find the indefinite integral. ​   ​

Accepted Answer

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

Question 13

Use integration by parts to find the integral below. ​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

​Find the capitalized cost C of an asset forever.The capitalized cost is given by   where   is the original investment,t is the time in years,   is the annual interest rate compounded continuously,​n is the total time in years over which the asset is capitalized,and   is the annual cost of maintenance (measured in dollars).Round your answer to two decimal places. ​

Accepted Answer

A)  ​$1,325,000 
B)  ​$1,075,000 
C)  ​$1,099,218.75 
D)  ​$908,333.33 
E)  ​$1,047,222.22 
A)  ​$1,325,000 
B)  ​$1,075,000 
C)  ​$1,099,218.75 
D)  ​$908,333.33 
E)  ​$1,047,222.22

Question 16

​The revenue (in dollars per year)for a new product is modeled by   where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar. ​

Accepted Answer

A)  ​$6,579 
B)  ​$3,291 
C)  ​$10,821 
D)  ​$15,830 
E)  ​$1,138 
A)  ​$6,579 
B)  ​$3,291 
C)  ​$10,821 
D)  ​$15,830 
E)  ​$1,138

Question 17

Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall. ​

Accepted Answer

A)  ​0.5734 
B)  ​0.5707 
C)  ​0.8547 
D)  ​0.9522 
E)  ​0.4257 
A)  ​0.5734 
B)  ​0.5707 
C)  ​0.8547 
D)  ​0.9522 
E)  ​0.4257

Question 18

Use Simpson's Rule to approximate the revenue for the marginal revenue function   with   Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places. ​

Accepted Answer

A)  1346.14 
B)  1230.4 
C)  678.36 
D)  1602.42 
E)  1439.03 
A)  1346.14 
B)  1230.4 
C)  678.36 
D)  1602.42 
E)  1439.03

Question 19

​Find the integral below using an integral table. ​
​   ​

Accepted Answer

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

Question 20

Use a table of integrals with forms involving   to find   ​

Accepted Answer

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

Approximate the definite integral "by hand," using the Trapezoidal Rule with trapezoids.Round answer to three decimal places.

The probability of recall in an experiment is modeled by , where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places.

Approximate the integral using Simpson's Rule: , Round your answer to three decimal places.

Find the indefinite integral.

Use the error formulas to find n such that the error in the approximation of the definite integral is less than 0.0001 using the Trapezoidal Rule.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Find the definite integral.

Use integration by parts to find the integral below. ,( , )

Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ,

The rate of change in the number of subscribers S to a newly introduced magazine is modeled by , where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years.

Identify u and dv for finding the integral using integration by parts.

Find the indefinite integral.

Use integration by parts to find the integral below.

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

The revenue (in dollars per year)for a new product is modeled by where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar.

Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.

Use Simpson's Rule to approximate the revenue for the marginal revenue function with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places.

Find the integral below using an integral table.

Use a table of integrals with forms involving to find

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

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Exam 6: Techniques of Integration

​Approximate the definite integral "by hand," using the Trapezoidal Rule with trapezoids.Round answer to three decimal places. ​

​The probability of recall in an experiment is modeled by , where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places. ​

​Approximate the integral using Simpson's Rule: , Round your answer to three decimal places. ​

Find the indefinite integral. ​ ​

Use the error formulas to find ​n such that the error in the approximation of the definite integral is less than 0.0001 using the Trapezoidal Rule. ​

​Determine whether the improper integral diverges or converges.Evaluate the integral if it converges. ​ ​

Find the definite integral. ​ ​

Use integration by parts to find the integral below. ​ ,( , ) ​

​Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ​ , ​

The rate of change in the number of subscribers S to a newly introduced magazine is modeled by , where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years. ​

Identify u and dv for finding the integral using integration by parts. ​

Find the indefinite integral. ​ ​

Use integration by parts to find the integral below. ​ ​

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

​The revenue (in dollars per year)for a new product is modeled by where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar. ​

Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall. ​

Use Simpson's Rule to approximate the revenue for the marginal revenue function with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places. ​

​Find the integral below using an integral table. ​ ​ ​

Use a table of integrals with forms involving to find ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Approximate the definite integral "by hand," using the Trapezoidal Rule with trapezoids.Round answer to three decimal places.

The probability of recall in an experiment is modeled by , where x is the percent of recall.What is the probability of recalling between 50% and 80%? Round your answer to three decimal places.

Approximate the integral using Simpson's Rule: , Round your answer to three decimal places.

Find the indefinite integral.

Use the error formulas to find n such that the error in the approximation of the definite integral is less than 0.0001 using the Trapezoidal Rule.

Determine whether the improper integral diverges or converges.Evaluate the integral if it converges.

Find the definite integral.

Use integration by parts to find the integral below. ,( , )

Determine the amount of money required to set up a charitable endowment that pays the amount P each year indefinitely for the annual interest rate compounded continuously. ,

The rate of change in the number of subscribers S to a newly introduced magazine is modeled by , where t is the time in years.Use Simpson's Rule with to estimate the total increase in the number of subscribers during the first 6 years.

Identify u and dv for finding the integral using integration by parts.

Find the indefinite integral.

Use integration by parts to find the integral below.

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

The revenue (in dollars per year)for a new product is modeled by where t the time in years.Estimate the total revenue from sales of the product over its first 3 years on the market.Round your answer to nearest dollar.

Suppose the mean height of American women between the ages of 30 and 39 is 64.5 inches,and the standard deviation is 2.7 inches.Use a symbolic integration utility to approximate the probability that a 30-to 39-year-old woman chosen at random is between 5 feet 4 inches and 6 feet tall.

Use Simpson's Rule to approximate the revenue for the marginal revenue function with Assume that the number of units sold,x,increases from 13 to 18.Round your answer to two decimal places.

Find the integral below using an integral table.

Use a table of integrals with forms involving to find