Sunday, May 22, 2011

Lower Sum

Another of the way to estimate the area below a curve y = f(x) for a < x < b is using the method of Lower 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 lowest point of the curve; while the width of the rectangle is $\inline \frac{b-a}{n}=\frac{5-0}{5}=1$. The summation of area of all the rectangles, b, gives to 19.5.

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.

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Betty, Created with GeoGebra