Is the function $f(x)=\sin(1/x)$ Lebesgue integrable on $(0,1]$?
I know that, as $f$ is continuous on the set, it is a measurable function. However, I'm stumped on how to go on. A nudge in the right direction would be greatly appreciated.
2026-04-15 09:33:37.1776245617
Is $\sin(1/x)$ Lebesgue integrable on $(0,1]$?
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Hint: $|f(x)|\le1$ for all $x\in(0,1]$, so $f$ is uniformly bounded.