I know how to prove(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\int\limits_0^{\infty} \frac{\sin(x)}{x}dx = \frac{\pi}{2}

[/tex]

using complex analysis, and I know how to prove

[tex]

\lim_{N\to\infty} 2N\sin\Big(\frac{x}{2N}\Big) = x

[/tex]

using series. I have some reason to believe, that if [itex]0<A<\pi[/itex], then

[tex]

\lim_{N\to\infty} \int\limits_0^{NA} \frac{\sin(x)}{2N\sin(\frac{x}{2N})} dx = \frac{\pi}{2},

[/tex]

but don't know how to prove this. Anyone knowing how to accomplish this?

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# Integrand approaching sin(x)/x

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