Sin 1 over x/Primitive function/Consider x^2 cos 1 over x/Exercise

We consider the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R} ,t\longmapsto f(t),$

with

${}f(t)={\begin{cases}0{\text{ for }}t=0,\\\sin {\frac {1}{t}}{\text{ for }}t\neq 0\,.\end{cases}}\,$

Show, with reference to the function

${}g(x)=x^{2}\cos {\frac {1}{x}}\,,$

that ${}f$ has an antiderivative.

Create a solution