Let $f$ be a function defined on $[0,1]$ by
$f(x) = { 0, \text{ if } x = 0} $ $f(x) = { x \sin \frac 1 x , \text{ if } 0 < x \leq 1} $
Prove that the curve $\{(x, f(x)) : x \in [0,1]\}$ is not rectifiable.
I'm not sure how to approach this. The general idea seems logical, we're proving that the length of the curve is infinite, but the method seems difficult to find.