iGCSE (2021 Edition)

# 12.06 Definite integrals and the area under a curve

Lesson
In this lesson we will show how integration can be used to calculate the exact area between the horizontal axis, a curve and two bounding values.

### The integral and the area

Let's explore the concept of using infinitely many rectangles to determine the area under a curve. If we increase the number of rectangles under a curve the accuracy of the area will also increase. The following applet demonstrates this. You may notice that approximating the area by using rectangles from above and below become closer as we increase the number of rectangles.

 Created with Geogebra

### Outcomes

#### 0606C14.10

Evaluate definite integrals and apply integration to the evaluation of plane areas.