Sunday, May 22, 2011

Upper Sum

One of the way to estimate the area below a curve y = f(x) for a < x < b is using the method of Upper Sum. In this method, we decide the number of rectangles to be built between x = a to x = b, which is denoted as n.

Look at the graph below, let's consider when n = 5 (5 rectangles are built). Do 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.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Betty, Created with GeoGebra

No comments:

Post a Comment