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Question Number 168800 by MikeH last updated on 17/Apr/22

$$\mathrm{If}\mathrm{the}\mathrm{function}f\mathrm{is}\mathrm{continuous}\mathrm{in}[a,b]$$$$\mathrm{express}\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\underset{k=1}{\sum ^n}f\left(\frac{k}{n}\right)\mathrm{as}\mathrm{a}\mathrm{definite}$$$$\mathrm{integral}.$$

Commented by safojontoshtemirov last updated on 18/Apr/22

$$\underset{n\to \mathrm{\infty }}{\lim }\frac{1}{n}\underset{k=1}{\sum ^n}f\left(\frac{k}{n}\right)=\underset{0}{\stackrel{1}{\int }}f\left(x\right)dx$$

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