In this last chapter of this course we will be taking a look at a couple of applications of integrals.  There are many other applications, however many of them require integration techniques that are typically taught in Calculus II.  We will therefore be focusing on applications that can be done only with knowledge taught in this course.

Because this chapter is focused on the applications of integrals it is assumed in all the examples that you are capable of doing the integrals.  There will not be as much detail in the integration process in the examples in this chapter as there was in the examples in the previous chapter.

Here is a listing of applications covered in this chapter.

Average Function Value  We can use integrals to determine the average value of a function.

Area Between Two Curves  In this section we’ll take a look at determining the area between two curves.

Volumes of Solids of Revolution / Method of Rings  This is the first of two sections devoted to find the volume of a solid of revolution.  In this section we look at the method of rings/disks.

Volumes of Solids of Revolution / Method of Cylinders  This is the second section devoted to finding the volume of a solid of revolution.  Here we will look at the method of cylinders.

More Volume Problems  In this section we’ll take a look at finding the volume of some solids that are either not solids of revolutions or are not easy to do as a solid of revolution.

Work  The final application we will look at is determining the amount of work required to move an object.