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Calculus II - Notes

Internet Explorer 10 & 11 Users : If you have been using Internet Explorer 10 or 11 to view the site (or did at one point anyway) then you know that the equations were not properly placed on the pages unless you put IE into "Compatibility Mode". I believe that I have partially figured out a way around that and have implimented the "fix" in the Algebra notes (not the practice/assignment problems yet). It's not perfect as some equations that are "inline" (i.e. equations that are in sentences as opposed to those on lines by themselves) are now shifted upwards or downwards slightly but it is better than it was.

If you wish to test this out please make sure the IE is not in Compatibility Mode and give it a test run in the Algebra notes. If you run into any problems please let me know. If things go well over the next week or two then I'll push the fix the full site. I'll also continue to see if I can get the inline equations to display properly.
 Next Chapter Applications of Integrals Next Section Integration by Parts

## Integration Techniques

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.

 Next Section Integration by Parts Next Chapter Applications of Integrals

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