Chapter 5.5, Problem 44ES

Define the function $f$ by

$f\left(x\right)=\left\{\begin{array}{cc}\frac{1}{x},& x\ne 0\\ 0,& x=0\end{array}\right.$

It follows from Theorem $\mathrm{5.5.8}\left(b\right)$ that $f$ is not integrable on the interval $\left[0,1\right]$ . Prove this to be the case by applying Definition $\mathrm{5.5.1}$ .