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−>∝) I_n = ∫


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

$l e t g i v e I_{n} = n \int_{1}^{1 + \frac{1}{n}} f (x^{n}) d x w i t h f i s n u m e r i c a l$ $f u n c t i o n i n t e g r a b l e o n [1, e] . p r o v e t h a t$ ${l i m}_{n - >\propto} I_{n} = \int_{1}^{e} \frac{f (t)}{t} d t .$
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