As promised, here is the full version of the previous "Counterexample to Fubini's Theorem" video, which can be found under the following link: https://youtu.be/cIpakZYdWjo
Fubini's theorem states that, under certain assumptions, the double integral of f(x,y) dx dy is equal to the double integral of f(x,y) dy dx. In this video, I give an example where Fubini's theorem does NOT apply, by explicitly showing that for a specific function, the two integrals are unequal. This is why it's very important to check that the assumptions of Fubini's theorem hold. The idea is that the function has a bad singularity at (0,0), which makes Fubini's theorem fail. Enjoy!
Video credit: The counterexample is taken from: http://www.math.jhu.edu/~jmb/note/nofub.pdf
