This week I will be teaching Year 12 (age 16-17) about the Trapezium Rule (Trapezoid US). An excellent resource for demonstrating this comes from zweigmedia.com as part of their online support for their Finite mathematics and Applied Calculus text. Using the numerical integration utility and grapher one can enter any function and calculate an integral as well as using numerical techniques such as the Trapezium Rule or Simpson’s Rule to the required accuracy. It is very easy to change the number of strips used demonstrating very clearly how this increases the accuracy. Depending on the nature of the curve it is easy to see why for example the Trapezium Rule might give an over or under-estimate. I will be directing my students to this site for checking their work and experimenting with differing numbers of strips, as well as reminding them how useful WolframAlpha is for checking integration – I have written a post for students here.
There are several other utilities available on this site, the Binomial Distribution utility provides a simple way to calculate Binomial probabilities and graph the distribution for example. I have also used the Normal calculator and the Linear Programming and Simplex tools.
This site also has many online tutorials and quizzes, I rather like the look of the Linear programming tutorial, this could be useful for students for self-study.