My text book asks me to prove that this is Riemann integrable. I can't figure out how to prove that, but anyway I'm far more interested in how to find the value of the integral on [0,1]. How would you go about that? Is it even possible?
2026-04-02 14:39:38.1775140778
How to calculate the integral from 0 to 1 of g(0):=0 and otherwise g(x)=sin(1/x)?
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HINT: Substitute $x=1/t$ and integrate by parts. The final result involves a cosine integral.