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.

Area under the graph

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.

Area under the graph

How to find the area bounded by a curve above the x-axis (tutorial 1) : ExamSolutions - youtube Video

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.

Area under the graph

Area bounded by a curve below the x-axis (tutorial 2) : ExamSolutions - youtube Video

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.

Area under the graph

Area bounded by a curve above and below the x-axis (tutorial 3) : ExamSolutions - youtube Video

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.
Area under the graph

How to find the area bounded by two curves (tutorial 4) : ExamSolutions - youtube Video