Question 1

Evaluate the integral.

Accepted Answer

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

Question 2

Evaluate the integral.

Accepted Answer

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

Question 3

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. B

Question 4

Evaluate

Accepted Answer

A)  0 
B)    
C)    
D)  ($\infty$) 
A)  0 
B)    
C)    
D)  ($\infty$)

Question 5

Evaluate the integral.

Accepted Answer

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

Question 6

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as   if   and either   Show all work.

Accepted Answer

Both x^p and p^x increase without bound as @#IMG-DLM&

Question 7

Find the partial fractions decomposition and an antiderivative.

Accepted Answer

partial fractions: @#IMG-DLM&

Question 8

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 0. 
D)  The integral evaluates to   . 
A)  The integral diverges. 
B)  The integral evaluates to   . 
C)  The integral evaluates to 0. 
D)  The integral evaluates to   .

Question 9

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 10

Evaluate the integral.

Accepted Answer

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

Question 11

Find an antiderivative.

Accepted Answer

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

Question 12

Find the limit.

Accepted Answer

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

Question 13

Evaluate the integral.

Accepted Answer

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

Question 14

Find the limit.

Accepted Answer

A)  1 
B)  8 
C)    
D)    
A)  1 
B)  8 
C)    
D)

Question 15

Find the partial fraction decomposition.

Accepted Answer

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

Question 16

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 17

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

Accepted Answer

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

Question 18

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 19

Find the value of c which will make the function   a pdf on the interval   .

Accepted Answer

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

Question 20

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

Evaluate the integral.

Evaluate the integral.

Determine whether or not the integral is improper.

Evaluate

Evaluate the integral.

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as if and either Show all work.

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

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

Determine whether or not the integral is improper.

Evaluate the integral.

Find an antiderivative.

Find the limit.

Evaluate the integral.

Find the limit.

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

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

Find the value of c which will make the function a pdf on the interval .

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

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

Evaluate the integral.

Evaluate the integral.

Determine whether or not the integral is improper.

Evaluate

Evaluate the integral.

Determine which function "dominates", where we say that the function f(x) dominates the function g(x) as if and either Show all work.

Find the partial fractions decomposition and an antiderivative.

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

Determine whether or not the integral is improper.

Evaluate the integral.

Find an antiderivative.

Find the limit.

Evaluate the integral.

Find the limit.

Find the partial fraction decomposition.

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

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

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

Find the value of c which will make the function a pdf on the interval .

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

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

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