Why is the integral of a function the area?

The integral of a function represents the area under the curve of that function. This is based on the fundamental concept of calculus known as the Riemann sum.

To understand this, imagine dividing a region bounded by a curve and the x-axis into small rectangles. The base of each rectangle is a small interval on the x-axis, and the height is determined by the value of the function at that point. By summing up the areas of all these rectangles, we get an approximation of the area under the curve.

As the width of the rectangles approaches zero (infinitely many rectangles), the approximation becomes more accurate. The integral of the function is defined as the limit of this summation process, giving us the exact area under the curve.

This fundamental connection between the integral and area is a key concept in calculus and allows us to use integration to find areas, among other applications.

Boost your grades with bespoke 3 day A Level Maths Easter Revision