Monday, September 19, 2011

Trapezoidal Sum

When upper sum and lower sum give a range of estimation to the area below a curve y = f(x) for a < x < b, Trapezoidal Sum uses n numbers of trapezoids to do the estimation of the area.

Look at the graph below, let's consider when n = 2 (2 trapezoids are built). Do take note that for each trapezoid, two points are taken from the left-ended value and right-ended value of the subinterval as part of the vertives. The summation of area of all the trapezoids, 12.47 square units.

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

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

Betty, Created with GeoGebra