... mathematical analysis... if ′′ f ′′ is Reimann integrable function on [a , b ] , then prove:: lim_(t→∞ ) {∫_a ^( b) f(x)cos(tx)dx }=0 ..Reimann−Lebesgue theorem...


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Question Number 128570 by mnjuly1970 last updated on 08/Jan/21
$... mathematical analysis... if ′′ f ′′ is Reimann integrable function on [a , b ] , then prove:: lim_(t→∞ ) {∫_a ^( b) f(x)cos(tx)dx }=0 ..Reimann−Lebesgue theorem...$
$. . . m a t h e m a t i c a l a n a l y s i s . . .$ $i f^{″} f^{″} i s R e i m a n n i n t e g r a b l e$ $f u n c t i o n o n [a, b], t h e n p r o v e ::$ ${l i m}_{t \to \infty} {\int_{a}^{b} f (x) c o s (t x) d x} = 0$ $. . R e i m a n n - L e b e s g u e t h e o r e m . . .$
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