let-give-I-n-n-1-1-1-n-f-x-n-dx-with-f-is-numerical-function-integrable-on-1-e-prove-that-lim-n-gt-I-n-1-e-f-t-t-dt-

Question Number 27497 by abdo imad last updated on 07/Jan/18

l e t g i v e I_{n} = n \int_{1}^{1 + \frac{1}{n}} f (x^{n}) d x w i t h f i s n u m e r i c a l

f u n c t i o n i n t e g r a b l e o n [1, e] . p r o v e t h a t

{l i m}_{n - >\propto} I_{n} = \int_{1}^{e} \frac{f (t)}{t} d t .