Upper Sum

One of the ways to estimate the area below a curve y = f (x) for a < x < b is using the method of Upper Sum. Here, we are going to look at the area estimation using this method by changing the number of rectangles (n) built between x = a to x = b.

Look at the graph below, let's consider when n = 5 (5 rectangles are built). Take note that for each rectangle, its height is taken from the y-value of the highest point of the curve; while the width of the rectangle is . The summation of area of all the rectangles, a, gives to 22.

If you slide the value of n to higher value, you may see that the rectangles are narrowed and the estimation of area below the curve is getting nearer to the actual area below the curve.


Betty, Created with GeoGebra