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.
Computing Definite Integrals We will take a look at the second part of the
Fundamental Theorem of Calculus in this section and start to compute definite
integrals.
Substitution Rule for Definite Integrals In this section we will revisit the
substitution rule as it applies to definite integrals.