Question 1

The integral   :

Accepted Answer

A)  diverges since the power of   is not less than 1. 
B)  converges since the power of   is greater than 1. 
C)  diverges since   . 
D)  converges since   . 
E)  none of the above 
A)  diverges since the power of   is not less than 1. 
B)  converges since the power of   is greater than 1. 
C)  diverges since   . 
D)  converges since   . 
E)  none of the above

Question 2

Which of the following integrals converges?

Accepted Answer

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

Question 3

For computing the integral   , the most efficient method is

Accepted Answer

A)  Integration by Parts with   and   . 
B)  substitution of   followed by Integration by Parts. 
C)  Integration by Parts, twice. 
D)  Integration by Parts with   and   . 
E)  None of the methods covered so far is efficient in computing this integral. 
A)  Integration by Parts with   and   . 
B)  substitution of   followed by Integration by Parts. 
C)  Integration by Parts, twice. 
D)  Integration by Parts with   and   . 
E)  None of the methods covered so far is efficient in computing this integral.

Question 4

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods.
A)   
B)

Accepted Answer

The answer of Evaluate the integrals using Integration by Parts,...

Question 5

Use the substitution   and the trigonometric identity   , or reduction formulas as necessary, to calculate the integrals. 
A)   
B)

Accepted Answer

The answer of Use the substitution   and the...

Question 6

Use the substitution   and the identity   to evaluate the integral   .

Accepted Answer

The answer of Use the substitution   and the...

Question 7

The time between customers at a checkout line is a random variable with exponential density. There is a 30% probability of waiting 5 min or more between customers. What is the average time between customers?

Accepted Answer

approximat

Question 8

Evaluate the integral using one or two methods, as indicated.
A)   : the Substitution Method followed by Integration by Parts, twice. 
B)   : Integration by Parts followed by the Substitution Method.

Accepted Answer

The answer of Evaluate the integral using one or two...

Question 9

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 10

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 11

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 12

Calculate   and   for the following. 
A)   
B)

Accepted Answer

The answer of Calculate   and   for...

Question 13

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 14

The partial fraction decomposition of   is:

Accepted Answer

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

Question 15

A cereal-packaging company fills boxes on average with 39 oz of cereal. Due to machine error, the actual volume is normally distributed with a standard deviation of
0.2 oz. Let   be the probability of a box having less than 38.5 oz. Express   as an integral of an appropriate density function and compute its value numerically.

Accepted Answer

The answer of A cereal-packaging company fills boxes on average...

Question 16

Compute the integral   .

Accepted Answer

The answer of Compute the integral   ....

Question 17

To show that   converges, we should use:

Accepted Answer

A)  the inequality   and the Comparison Test. 
B)  the inequality   and the Comparison Test. 
C)  evaluation of the integral. 
D)  No method can be used, since the function   is not non-negative. 
E)  none of the above. 
A)  the inequality   and the Comparison Test. 
B)  the inequality   and the Comparison Test. 
C)  evaluation of the integral. 
D)  No method can be used, since the function   is not non-negative. 
E)  none of the above.

Question 18

The height of sixth grade students in a certain class is a random variable   with mean   in. Assume the height of the students is normally distributed with standard deviation   in. Let   be the probability that a student will be at least   in. tall. Express   as an integral of an appropriate density function, and compute its value numerically.

Accepted Answer

The answer of The height of sixth grade students in...

Question 19

Evaluate the integral   .

Accepted Answer

The answer of Evaluate the integral   ....

Question 20

The height of sixth grade students in a class is a random variable   with mean   in. Assume the height of the students is normally distributed with standard deviation   in. Let   be the probability that a student will be at most   in. tall. Express   as an integral of an appropriate density function, and compute its value numerically.

Accepted Answer

The answer of The height of sixth grade students in...

The integral :

Which of the following integrals converges?

For computing the integral , the most efficient method is

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods. A) B)

Use the substitution and the trigonometric identity , or reduction formulas as necessary, to calculate the integrals. A) B)

Use the substitution and the identity to evaluate the integral .

The time between customers at a checkout line is a random variable with exponential density. There is a 30% probability of waiting 5 min or more between customers. What is the average time between customers?

Evaluate the integral using one or two methods, as indicated. A) : the Substitution Method followed by Integration by Parts, twice. B) : Integration by Parts followed by the Substitution Method.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Calculate and for the following. A) B)

Evaluate the integral .

The partial fraction decomposition of $The partial fraction decomposition of is:$ is:

Compute the integral .

To show that converges, we should use:

Evaluate the integral .

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

Exam 8: Techniques of Integration

The integral :

Which of the following integrals converges?

For computing the integral , the most efficient method is

Evaluate the integrals using Integration by Parts, the Substitution Method, or both methods. A) B)

Use the substitution and the trigonometric identity , or reduction formulas as necessary, to calculate the integrals. A) B)

Use the substitution and the identity to evaluate the integral .

The time between customers at a checkout line is a random variable with exponential density. There is a 30% probability of waiting 5 min or more between customers. What is the average time between customers?

Evaluate the integral using one or two methods, as indicated. A) : the Substitution Method followed by Integration by Parts, twice. B) : Integration by Parts followed by the Substitution Method.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Calculate and for the following. A) B)

Evaluate the integral .

The partial fraction decomposition of is:

Compute the integral .

To show that converges, we should use:

Evaluate the integral .

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

The partial fraction decomposition of $The partial fraction decomposition of is:$ is: