How to Approximate the area under a curve using rectangles
The idea of finding the area under a curve is an important fundamental concept in calculus. Consider a function y = f(x). Now the area under the curve is to be calculated. The area under a curve problem is stated as 'Let f(x) be non negative on [a, b]. Find the area of the region lying beneath the curve y = f(x) and above the x-axes, from x = a to x = b. Note that finding the area under a curve will imply that you are dealing with a non negative function. The way to approach is to divide the entire interval between a and b into sub intervals there by construction small rectangles side by side. Now the area under the curve can be approximated as the sum of the areas of the individual rectangles. The smaller the width of the rectangles the more precise your final answer will be. This video shows how to approximate the area under a curve using rectangles.