Students will approximate the area under a curve using Riemann sums. This will be done by utilizing a program that computes the Riemann sum as well as drawing the graphical representation. The activity concludes with students discovering that if enough Riemann sums are used, then the area under a curve can be calculated with the required degree of precision.

http://education.ti.com/educationportal/activityexchange/Activity.do?cid...

From Sean Bird's website: "Put this [TI-Nspire] file in MyLib so that you can access the area approximation methods from any document."
The program will find the approximate areas for the left, right and midpt Reimann sums, as well as the trapezoid, Simpsons and numeric integral areas.
http://cs3.covenantchristian.org/bird/TTT/NspireCalc/area.tns

For other TI-Nspire files from Sean's website, visit:
http://cs3.covenantchristian.org/bird/Nspire.html

Choose a function and see the effect on the Riemann sum when you change the slice width. The file itself can be downloaded and installed on your computer or network.
http://www.vias.org/simulations/simusoft_riemannsum.html

This animation from Lou Talman is a dynamic representation of the area function we introduce in the standard proof of the Fundamental Theorem of Calculus.
http://clem.mscd.edu/~talmanl/HTML/FTOC.html

Riemann Sums 1
Define the function f(1). Then use trap(b,a,n) to find the area under the function between a and b with n divisions using the trapezoidal rule. The function lrs(b,a,n) uses the lefthand rule, rrs(b,a,n) uses the righthand rule and sr(b,a,n) uses Simpson's Rule. How cool is that!

http://mathplotter.lawrenceville.org/mathplotter/mathPage/riemann.htm

A lovely Geogebra java applet from Miguel Bayona, The Lawrenceville School, Lawrenceville, NJ. It demonstrates the lower sum, upper sum, left sum, right sum, midpoint sum and trapezoidal sum for a function of your choosing. Loading the applet can take a while, so be patient.