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Online Notes / Calculus I (Notes) / Integrals

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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.

Online Notes / Calculus I (Notes) / Integrals

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