Question Number 129870 by Bird last updated on 20/Jan/21
![f continue on [0^ 1] calculate lim_(n→+∞) (1/n)Σ_(k=0) ^n (n−k)∫_(k/n) ^((k+1)/n) f(x)dx](https://www.tinkutara.com/question/Q129870.png)
$${f}\:{continue}\:{on}\:\left[\bar {\mathrm{0}1}\right]\:{calculate} \\ $$$${lim}_{{n}\rightarrow+\infty} \frac{\mathrm{1}}{{n}}\sum_{{k}=\mathrm{0}} ^{{n}} \left({n}−{k}\right)\int_{\frac{{k}}{{n}}} ^{\frac{{k}+\mathrm{1}}{{n}}} {f}\left({x}\right){dx} \\ $$