Prove that for all real numbers a and b with a<b, the following inequality holds; (∫_a ^b 1 dx)^3 ≤ (b−a)(∫_a ^b (x−a+1)^2 dx)(∫


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Question Number 218626 by Nicholas666 last updated on 13/Apr/25

$P r o v e t h a t f o r a l l r e a l n u m b e r s a a n d b$ $w i t h a < b, t h e f o l l o w i n g i n e q u a l i t y h o l d s;$ ${(\int_{a}^{b} 1 d x)}^{3} ⩽ (b - a) (\int_{a}^{b} {(x - a + 1)}^{2} d x) (\int_{a}^{b} \frac{1}{{(a - x + 1)}^{3}} d x)$
Commented by Nicholas666 last updated on 14/Apr/25

$f o r t h o s e o f y o u w h o m a r k e d t h e$ $p r o b l e m I p o s t e d i n R e d {i t}^{'} s b e c a u s e$ $Y o u {d i d n}^{'} t b r e a k d o w n t h e m a t h w i t h$ $i n d e p t h a n a l y s i s .$
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