The applet below shows the relationship among the area under the curve, the lower sum, and the upper sum. As the number of rectangles (

*n*) increases, the sum of the areas of the rectangles get closer and closer to the actual area under the curve.
Guillermo Bautista Jr. , Created with GeoGebra

The method of approximation above is called the

*Riemann Sum*. It was named after Bernhard Riemann, a German mathematician.

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