Demonstration of the orthogonality of the trigonometric functions

Integrating

Demonstrating that the integral goes to zero for m≠n and λ/2 if m=n (we demonstrate this by using random choices for m and n)

If we run the above command enough times, we will see  that results where n=m give indeterminate values, for these we should use a Limit.

Performing the same steps for   and  

Created by Wolfram Mathematica 6.0  (24 October 2007)