Paul's Online Math Notes
     
 
Online Notes / Calculus II (Notes) / Integration Techniques
Notice
I've been notified that Lamar University will be doing some network maintenance on the following days.
  • Sunday November 9th 2014 from 12:05 AM until 11:59 AM Central Daylight Time
  • Sunday November 16th 2014 from 4:0 AM until 11:59 AM Central Daylight Time

During these times the site will either be completely unavailable or you will receive an error when trying to access any of the notes and/or problem pages. I realize this is probably a bad time for many of you but I have no control over this kind of thing and there are really no good times for this to happen and they picked the time that would cause the least disruptions for the fewest people. I apologize for the inconvenience!

Paul.



Internet Explorer 10 & 11 Users : If you are using Internet Explorer 10 or Internet Explorer 11 then, in all likelihood, the equations on the pages are all shifted downward. To fix this you need to put your browser in Compatibility View for my site. Click here for instructions on how to do that. Alternatively, you can also view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.

Calculus II - Notes Integration by Parts

In this chapter we are going to be looking at various integration techniques.  There are a fair number of them and some will be easier than others.  The point of the chapter is to teach you these new techniques and so this chapter assumes that you’ve got a fairly good working knowledge of basic integration as well as substitutions with integrals.  In fact, most integrals involving “simple” substitutions will not have any of the substitution work shown.  It is going to be assumed that you can verify the substitution portion of the integration yourself.

 

Also, most of the integrals done in this chapter will be indefinite integrals.  It is also assumed that once you can do the indefinite integrals you can also do the definite integrals and so to conserve space we concentrate mostly on indefinite integrals.  There is one exception to this and that is the Trig Substitution section and in this case there are some subtleties involved with definite integrals that we’re going to have to watch out for.  Outside of that however, most sections will have at most one definite integral example and some sections will not have any definite integral examples.

 

Here is a list of topics that are covered in this chapter.

 

Integration by Parts  Of all the integration techniques covered in this chapter this is probably the one that students are most likely to run into down the road in other classes.

 

Integrals Involving Trig Functions  In this section we look at integrating certain products and quotients of trig functions.

 

Trig Substitutions  Here we will look using substitutions involving trig functions and how they can be used to simplify certain integrals.

 

Partial Fractions  We will use partial fractions to allow us to do integrals involving some rational functions.

 

Integrals Involving Roots  We will take a look at a substitution that can, on occasion, be used with integrals involving roots.

 

Integrals Involving Quadratics  In this section we are going to look at some integrals that involve quadratics.

 

Integration Strategy  We give a general set of guidelines for determining how to evaluate an integral.

 

Improper Integrals  We will look at integrals with infinite intervals of integration and integrals with discontinuous integrands in this section.

 

Comparison Test for Improper Integrals  Here we will use the Comparison Test to determine if improper integrals converge or diverge.

 

Approximating Definite Integrals  There are many ways to approximate the value of a definite integral.  We will look at three of them in this section.

Calculus II - Notes Integration by Parts

Online Notes / Calculus II (Notes) / Integration Techniques

[Contact Me] [Links] [Privacy Statement] [Site Map] [Terms of Use] [Menus by Milonic]

© 2003 - 2014 Paul Dawkins