This applet shows upper and lower Riemann Sums as well as the exact integration of the area under a curve. It is very similar to the ways that both Cavalieri and Wallis approximated integration as is discussed in the history section.
Integration between two irregular curves.
This applet shows different irregularly shaped areas that can be exactly defined by integration. It is similar in nature (just in 2 dimensions, not 3) to the way scientists often find the volume of large objects as explained in the application section.
