Originally Posted by
rrra
Well I like your challenge. So I'll give the math problem a go since I don't know engineering or biology. It is quite easy. The Dirichlet function is a type of nowhere continuous function, which means what it says. To be reimann integrable, a function must have finitely many discontinuities. Therefore the Dirichlet function (which has nothing but discontinuities) is not reimann integrable. Don't ask me for a proof as I haven't done any formal math in several years, although it probably wouldnt be that difficult.