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

Evaluate the integral. (Hint: you may need to use a reduction formula.)

Accepted Answer

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

Question 5

Find the error in the following incorrect calculation.

Accepted Answer

Rewrite @#IMG-DLM& ,
Since @#IMG-DLM& and @#IMG-DLM& , @#IMG-DLM& (the

Question 6

Evaluate the integral.

Accepted Answer

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

Question 7

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 8

Evaluate the integral.

Accepted Answer

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

Question 9

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 10

Find the limit.

Accepted Answer

A)  1 
B)    
C)    
D)    
A)  1 
B)    
C)    
D)

Question 11

Evaluate the integral.

Accepted Answer

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

Question 12

Find the mean of x, given the pdf   ,   . Round your answer to three decimal places.

Accepted Answer

A)  0.062 
B)  0.500 
C)  0.031 
D)  undefined 
A)  0.062 
B)  0.500 
C)  0.031 
D)  undefined

Question 13

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

Accepted Answer

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

Question 14

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 15

Find an antiderivative.

Accepted Answer

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

Question 16

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 17

Evaluate the integral.

Accepted Answer

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

Question 18

Use an integral formula to evaluate the integral.

Accepted Answer

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

Question 19

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 20

Find the indicated limit.

Accepted Answer

A)  0 
B)    
C)    
D)  limit does not exist 
A)  0 
B)    
C)    
D)  limit does not exist

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

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

Evaluate the integral.

Evaluate the integral. (Hint: you may need to use a reduction formula.)

Find the error in the following incorrect calculation.

Evaluate the integral.

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

Evaluate the integral.

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

Find the limit.

Evaluate the integral.

Find the mean of x, given the pdf , . Round your answer to three decimal places.

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

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

Find an antiderivative.

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.

Use an integral formula to evaluate the integral.

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

Find the indicated limit.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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 8: Integration Techniques

Find the partial fraction decomposition.

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

Evaluate the integral.

Evaluate the integral. (Hint: you may need to use a reduction formula.)

Find the error in the following incorrect calculation.

Evaluate the integral.

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

Evaluate the integral.

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

Find the limit.

Evaluate the integral.

Find the mean of x, given the pdf , . Round your answer to three decimal places.

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

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

Find an antiderivative.

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.

Use an integral formula to evaluate the integral.

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

Find the indicated limit.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

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. $Find the partial fraction decomposition.$