Riemann Sums

Choose any function and type it into the f(x) input box below. Select the left or right sum checkboxes in order to view the respective sums. The values a and b are the lower and upper values for x that the function will display, and Box represents the number of boxes used for the sum.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

How might the boxes in the Riemann Sum help us estimate the area under the curves?
Is it better to use more or less boxes to approximate the area under a curve/function?
Why might we use the Left Sum versus the Right Sum? Does it matter?

Alycia Jacobson, 29 October 2013, Created with GeoGebra