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Question Number 197562 by universe last updated on 21/Sep/23

$$\mathrm{let}{\mathrm{f}}_{\mathrm{n}}\left(\mathrm{x}\right)={\mathrm{nsin}}^{2\mathrm{n}+1}\mathrm{x}\cos \mathrm{x}\mathrm{then}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\underset{n\to \mathrm{\infty }}{\lim }{\int }_0^{\pi /2}{\mathrm{f}}_{\mathrm{n}}\left(\mathrm{x}\right)\mathrm{dx}-{\int }_0^{\pi /2}\left(\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }{\mathrm{f}}_{\mathrm{n}}\left(\mathrm{x}\right)\right)\mathrm{dx}=?$$

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