Problem:
Graphically illustrate the approximation of the integral

using the Simpson's Rule.

Visualization:

[Press this to see animation again!]

In the animation above, first you can see how by increasing the number of equal-sized intervals the sum of the areas of parabolas can better approximate the integral.

The following table indicates the sums of the various areas of the parabolas n indicates one half the number of parabolas.

nSum of areas of
parabolas
40.79420139
80.77495438
160.77364287
320.77356744
640.77356283
1280.77356255
2560.77356253
5120.77356253
10240.77356253

0.77356253 appears to be a reasonable estimate of our integral.