If-the-function-f-is-continuous-in-a-b-express-lim-n-1-n-k-1-n-f-k-n-as-a-definite-integral-

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

If the function f is continuous in [a, b]

express \lim_{n \to \infty} \frac{1}{n} \underset{k = 1}{\sum^{n}} f (\frac{k}{n}) as a definite

integral .

Commented by safojontoshtemirov last updated on 18/Apr/22

\lim_{n \to \infty} \frac{1}{n} \underset{k = 1}{\sum^{n}} f (\frac{k}{n}) = \underset{0}{\int^{1}} f (x) d x