Question 1

Use the table values and apply the Simpson's Rule to approximate   to one decimal place.   ​​

Accepted Answer

A) 1.7 
B) 1.6 
C) 1.3 
D) 2.0 
E) 2.3 
A) 1.7 
B) 1.6 
C) 1.3 
D) 2.0 
E) 2.3

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

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

Accepted Answer

A) 65.4 
B) 32.7 
C) 21.8 
D) 10.9 
E) 3.6 
A) 65.4 
B) 32.7 
C) 21.8 
D) 10.9 
E) 3.6

Question 4

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 5

Evaluate the definite integral   . ​

Accepted Answer

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

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​   ​

Accepted Answer

A) 49 
B) 50 
C) 8 
D) 7 
E) does not exist 
A) 49 
B) 50 
C) 8 
D) 7 
E) does not exist

Question 8

Equations are given whose graphs enclose a region. Find the area of the region. ​   ,   ​

Accepted Answer

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

Question 9

For what value of c does ?   ​

Accepted Answer

A) 16 
B) 384 
C) ​-8 
D) 8 
E) -16 
A) 16 
B) 384 
C) ​-8 
D) 8 
E) -16

Question 10

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the right-hand endpoints of the subintervals. Compute the approximate area using up to four decimal places as needed. ​   from   to     subintervals.
​

Accepted Answer

A) 9.25 square units 
B) 17.5 square units 
C) 0.5 square unit 
D) 21 square units 
E) 37 square units 
A) 9.25 square units 
B) 17.5 square units 
C) 0.5 square unit 
D) 21 square units 
E) 37 square units

Question 11

Evaluate the definite integral   . ​

Accepted Answer

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

Question 12

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 13

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 14

Find the average value of the function   ​

Accepted Answer

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

Question 15

Evaluate the integral   . ​

Accepted Answer

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

Question 16

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

Accepted Answer

A) 2,000 
B) 1,000 
C) 4,000 
D) 40,000 
E) 20,000 
A) 2,000 
B) 1,000 
C) 4,000 
D) 40,000 
E) 20,000

Question 17

Evaluate the integral   . ​

Accepted Answer

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

Question 18

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 19

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by   (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by   . ​

Accepted Answer

A) $107,619.44 
B) $247,524.72 
C) $63,305.55 
D) $333,620.27 
E) $150,667.22 
A) $107,619.44 
B) $247,524.72 
C) $63,305.55 
D) $333,620.27 
E) $150,667.22

Question 20

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

Use the table values and apply the Simpson's Rule to approximate to one decimal place.

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.

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

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

Evaluate the definite integral .

Evaluate the integral .

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Equations are given whose graphs enclose a region. Find the area of the region. ,

For what value of c does ?

Approximate the area under the curve over the specified interval by using the indicated number of subintervals (or rectangles) and evaluating the function at the right-hand endpoints of the subintervals. Compute the approximate area using up to four decimal places as needed. from to subintervals.

Evaluate the definite integral .

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 .

Find the average value of the function

Evaluate the integral .

For what value of c is the function a probability density function?

Evaluate the integral .

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

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

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 the table values and apply the Simpson's Rule to approximate to one decimal place. ​​

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. ​

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

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

Evaluate the definite integral . ​

Evaluate the integral . ​

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1. ​ ​

Equations are given whose graphs enclose a region. Find the area of the region. ​ , ​

For what value of c does ? ​

Evaluate the definite integral . ​

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 . ​

Find the average value of the function ​

Evaluate the integral . ​

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

Evaluate the integral . ​

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by . ​

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

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 the table values and apply the Simpson's Rule to approximate to one decimal place.

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.

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

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

Evaluate the definite integral .

Evaluate the integral .

Find the area, if it exists, of the region under the graph of y=f(x) and to the right of x=1.

Equations are given whose graphs enclose a region. Find the area of the region. ,

For what value of c does ?

Evaluate the definite integral .

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 .

Find the average value of the function

Evaluate the integral .

For what value of c is the function a probability density function?

Evaluate the integral .

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

The production from a particular assembly line is considered a continuous income stream with annual rate of flow given by (in thousands of dollars per year). Use Simpson's Rule with n = 4 to approximate the total income to 2 decimal places over the first 2 years, given by .

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