Integration is the reverse process of differentiation. Geometrically, it is represented by the area between the curve and the x-axis. This will be further explained in our section Applications of Integration.

 

However, unlike differentiation, integration is not as easy as just following a certain set of rules. Rather, it is about observation--manipulating the integrand to a standard form before performing integration. This is not always an easy task. However, do note that sometimes, the integrand is nothing close to a standard form, and other methods will have to be employed.

 

Our discussion of integration will be as follows: In this section, we will introduce and identify the major standard functions and their forms. Slight manipulation techniques may be needed to solve some of the problems. Next, we will discuss the applications of integration, particularly the area bounded by curves and volumes of revolution. The applications are not limited to these two.

 

 

Notation and Terms

 

Integration is represented by:

                                                   

 

                is the indefinite integral

c                            is the arbitrary constant

f(x)                        is the integrand

                         is the integral sign