∫f(x)g(x)dx=Σ_(n=0) ^∞ (−1)^n lim_(h→0) (1/h^n ) Σ_(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


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

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