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Question Number 53476 by maxmathsup by imad last updated on 22/Jan/19

let f(x)=∫_0 ^x  t(√(2t−1))dt    calculate ∣sup_(1≤x≤2)  f(x) −inf_(1≤x≤2) f(x)∣

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{t}\sqrt{\mathrm{2}{t}−\mathrm{1}}{dt}\:\:\:\:{calculate}\:\mid{sup}_{\mathrm{1}\leqslant{x}\leqslant\mathrm{2}} \:{f}\left({x}\right)\:−{inf}_{\mathrm{1}\leqslant{x}\leqslant\mathrm{2}} {f}\left({x}\right)\mid \\ $$

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