Question Number 111770 by mathmax by abdo last updated on 04/Sep/20
![f function continue on [0,1] find lim_(n→+∞) (1/n)Σ_(k=0) ^n (n−k)∫_(k/n) ^((k+1)/n) f(x)dx](https://www.tinkutara.com/question/Q111770.png)
$$\mathrm{f}\:\mathrm{function}\:\mathrm{continue}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{\mathrm{n}}\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \left(\mathrm{n}−\mathrm{k}\right)\int_{\frac{\mathrm{k}}{\mathrm{n}}} ^{\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$