Question 1

Find the partial fraction decomposition.

Accepted Answer

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

Question 2

Use a comparison to determine whether the integral converges or diverges.

Accepted Answer

A)  The integral converges. 
B)  The integral diverges. 
A)  The integral converges. 
B)  The integral diverges.

Question 3

Evaluate the integral.

Accepted Answer

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

Question 4

Use a table of integrals to find an antiderivative.

Accepted Answer

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

Question 5

Find   where

Accepted Answer

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

Question 6

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer   ,   (Use integration by parts with   ).

Accepted Answer

The answer of Several useful integration formulas called reduction formulas...

Question 7

Evaluate the integral using integration by parts and substitution.

Accepted Answer

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

Question 8

Determine whether or not the integral is improper.

Accepted Answer

A)  The integral is improper. 
B)  The integral is not improper. 
A)  The integral is improper. 
B)  The integral is not improper.

Question 9

Evaluate the integral.

Accepted Answer

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

Question 10

Evaluate the integral.

Accepted Answer

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

Question 11

The mean   (one measure of average) of a random variable with pdf   on the interval   is     . Find the mean if   .

Accepted Answer

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

Question 12

Find the partial fraction decomposition.

Accepted Answer

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

Question 13

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Accepted Answer

A)  converges to   
B)  converges to   
C)  converges to   
D)  diverges 
A)  converges to   
B)  converges to   
C)  converges to   
D)  diverges

Question 14

Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

Accepted Answer

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

Question 15

Evaluate the integral.

Accepted Answer

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

Question 16

Use a table of integrals to evaluate the definite integral.

Accepted Answer

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

Question 17

Evaluate the integral.

Accepted Answer

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

Question 18

Find the partial fraction decomposition.

Accepted Answer

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

Question 19

Find the partial fraction decomposition.

Accepted Answer

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

Question 20

Evaluate the integral.

Accepted Answer

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

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Use a comparison to determine whether the integral converges or diverges.

Evaluate the integral.

Use a table of integrals to find an antiderivative.

Find where

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer , (Use integration by parts with ).

Evaluate the integral using integration by parts and substitution.

Determine whether or not the integral is improper.

Evaluate the integral.

Evaluate the integral.

The mean (one measure of average) of a random variable with pdf on the interval is . Find the mean if .

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

Evaluate the integral.

Use a table of integrals to evaluate the definite integral.

Evaluate the integral.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Evaluate the integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 7: Integration Techniques

Find the partial fraction decomposition.

Use a comparison to determine whether the integral converges or diverges.

Evaluate the integral.

Use a table of integrals to find an antiderivative.

Find where

Several useful integration formulas called reduction formulas are used to automate the process of performing multiple integrations by parts. Prove that for any positive integer , (Use integration by parts with ).

Evaluate the integral using integration by parts and substitution.

Determine whether or not the integral is improper.

Evaluate the integral.

Evaluate the integral.

The mean (one measure of average) of a random variable with pdf on the interval is . Find the mean if .

Find the partial fraction decomposition.

Determine whether the integral converges or diverges. Find the value of the integral if it converges.

Evaluate the integral using integration by parts and substitution (as we recommended in the text, "Try something!").

Evaluate the integral.

Use a table of integrals to evaluate the definite integral.

Evaluate the integral.

Find the partial fraction decomposition.

Find the partial fraction decomposition.

Evaluate the integral.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the partial fraction decomposition. $Find the partial fraction decomposition.$