f-x-g-x-dx-n-0-1-n-lim-h-0-1-h-n-i-o-n-1-i-n-i-n-i-f-x-n-i-h-1-n-a-x-x-t-n-g-t-dt-prove-that-right-its-a-relation-that-i-have-derrived-

Question Number 207924 by AliJumaa last updated on 31/May/24

\int f (x) g (x) d x = \underset{n = 0}{\sum^{\infty}} {(- 1)}^{n} \lim_{h \to 0} \frac{1}{h^{n}} \underset{i = o}{\sum^{n}} [{(- 1)}^{i} (\frac{n!}{i! (n - i)!}) f (x + (n - i) h)] \frac{1}{n!} \underset{a}{\int^{x}} {(x - t)}^{n} g (t) d t

p r o v e t h a t r i g h t

i t s a r e l a t i o n t h a t i h a v e d e r r i v e d