Problem:
Graphically illustrate the approximation of the integral

using the Trapezoidal 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 trapezoids can better approximate the integral.

The following table indicates the sums of the various areas of the trapezoids n indicates the number of trapezoids.

nSum of areas of
trapezoids
40.43358
80.70404
160.75723
320.76954
640.77256
1280.77331
2560.77350
5120.77355
10240.77356
20480.77356

0.77356 appears to be a reasonable estimate of our integral.