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\[f(x) = sin\Big( lim_{ t \rightarrow 0} \frac{2x}{\pi} cot^{-1}\frac{x}{t^{2}}\Big)\]

then

\[\int_a^b f(x)dx = \]

here \[a = \frac{-\pi}{2} , b = \frac{\pi}{2}\]

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