$$\lim_{n\to\infty} \int_0^{\pi/2} \frac{\sin^2(nx)}{1+x} \,dx$$
2026-03-28 17:05:55.1774717555
limit value ! solution in detail please
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Hint:
You can decompose the domain of integration in $\dfrac n2$ half-periods of the sine and use constant upper and lower bounds of the denominator (it is monotonous) in each of them. Then use that the average value of the integral of the squared sine is $\dfrac12$, sum for all periods and squeeze.