Integrals
In this chapter we will be looking at integrals. Integrals
are the third and final major topic that will be covered in this class. As with
derivatives this chapter will be devoted almost exclusively to finding and
computing integrals. Applications will be given in the following chapter.
There are really two types of integrals that we�ll be looking at in this chapter
: Indefinite Integrals and Definite Integrals. The first half of this chapter
is devoted to indefinite integrals and the last half is devoted to definite
integrals. As we will see in the last half of the chapter if we don�t know
indefinite integrals we will not be able to do definite integrals.
Here is a quick listing of the material that is in this
chapter.
Indefinite Integrals - In
this section we will start with the definition of indefinite integral. This
section will be devoted mostly to the definition and properties of indefinite
integrals.
Computing Indefinite Integrals - In
this section we will compute some indefinite integrals and take a look at a
quick application of indefinite integrals.
Substitution Rule for Indefinite Integrals
- Here
we will look at the Substitution Rule as it applies to indefinite integrals.
Many of the integrals that we�ll be doing later on in the course and in later
courses will require use of the substitution rule.
More Substitution Rule - Even
more substitution rule problems.
Area
Problem - In
this section we start off with the motivation for definite integrals and give
one of the interpretations of definite integrals.
Definition of the Definite Integral - We
will formally define the definite integral in this section and give many of its
properties. We will also take a look at the first part of the Fundamental
Theorem of Calculus.
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