$\lim\limits_{n\to\infty}\int_{1/n}^ne^{-x}\cos(\frac{\pi}{2nx})dx$

Question

How can I prove $\lim\limits_{n\to\infty}\int_{1/n}^ne^{-x}\cos(\frac{\pi}{2nx})dx$=1?
I already proved $\lim\limits_{n\to\infty}\int_{1/n}^ne^{-x}\cos(\frac{\pi}{2nx})dx\leq 1$

Answer 1

It’s a Schlomilch integral Hence the result is 1

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