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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 that 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 find 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.