Lecture 24.2 - Examples of Integrable and Non-Integrable Functions

In this video, we use the definition of the Darboux integral directly to show that the integral of f(x) = x^2 from 0 to b is b^3/3, as we would expect. We also show that the function defined to take the value 1 for rational values of x and 0 for irrational values of x is not integrable.