Question 1

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

Accepted Answer

A)  converges to 0 
B)  converges to   
C)  converges to   
D)  diverges 
A)  converges to 0 
B)  converges to   
C)  converges to   
D)  diverges

Question 2

Find an antiderivative.

Accepted Answer

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

Question 3

Evaluate the integral.

Accepted Answer

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

Question 4

Evaluate the integral.

Accepted Answer

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

Question 5

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 6

Evaluate the integral.

Accepted Answer

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

Question 7

A function   is a probability density function (pdf) on the interval   if   Find the value of the constant   to make the function   a pdf on the interval   .

Accepted Answer

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

Question 8

Evaluate the integral.

Accepted Answer

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

Question 9

Evaluate the integral.

Accepted Answer

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

Question 10

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

Accepted Answer

A)  converges to   
B)  converges to 0 
C)  converges to   
D)  diverges 
A)  converges to   
B)  converges to 0 
C)  converges to   
D)  diverges

Question 11

Evaluate the integral.

Accepted Answer

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

Question 12

Evaluate the integral.

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)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   . 
A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   .

Question 14

Evaluate the integral.

Accepted Answer

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

Question 15

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

Accepted Answer

A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   . 
A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to   . 
D)  The integral evaluates to   .

Question 16

Use an integral formula to evaluate the integral.

Accepted Answer

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

Question 17

Find the partial fractions decomposition and an antiderivative.

Accepted Answer

partial fractions: @#IMG-DLM&

Question 18

Evaluate the integral.

Accepted Answer

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

Question 19

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 20

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

Accepted Answer

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

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

Find an antiderivative.

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

A function is a probability density function (pdf) on the interval if Find the value of the constant to make the function a pdf on the interval .

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

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

Use an integral formula to evaluate the integral.

Find the partial fractions decomposition and an antiderivative. $Find the partial fractions decomposition and an antiderivative.$

Evaluate the integral.

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

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

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

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

Find an antiderivative.

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

A function is a probability density function (pdf) on the interval if Find the value of the constant to make the function a pdf on the interval .

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

Evaluate the integral.

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

Evaluate the integral.

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

Use an integral formula to evaluate the integral.

Find the partial fractions decomposition and an antiderivative.

Evaluate the integral.

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

You are given a pair of integrals below. Evaluate the integral that can be worked using the techniques covered so far (the other cannot).

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 fractions decomposition and an antiderivative. $Find the partial fractions decomposition and an antiderivative.$