Question Number 50407 by Abdo msup. last updated on 16/Dec/18
$${determine}\:{f}\:\in{C}^{\mathrm{0}} \left(\left[\mathrm{0},\mathrm{1}\right],{R}\right)\:{verifying} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:=\frac{\mathrm{1}}{\mathrm{3}}\:+\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\left({f}\left({x}^{\mathrm{2}} \right)\right)^{\mathrm{2}} {dx} \\ $$