Integration – Area under a graph

Integration can be used to find the area bounded by a curve y = f(x), the x-axis and the lines x=a and x=b by using the following method.

However, you must be very careful in the way you use this as the following examples will show.

Area bounded by a curve when it is above the x-axis

In this tutorial I show you how to find the area bounded by a curve when it is above the x-axis.

Find the area:

Finding the area below the x-axis

In this tutorial I show you how to find the area bounded by a curve when it is below the x-axis.

Find the area:

Finding an area above and below the x-axis

In this tutorial I show you how to find the area bounded by a curve when it is partly below the x-axis and partly above the x-axis using the following example.

Find the area:

Finding the area bounded by two curves

In this tutorial I show you several ways of how to find the area bounded by two curves using the following example.

Find the area: