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determine-f-C-0-0-1-R-verifying-0-1-f-x-dx-1-3-0-1-f-x-2-2-dx-




Question Number 50407 by Abdo msup. last updated on 16/Dec/18
determine f ∈C^0 ([0,1],R) verifying  ∫_0 ^1 f(x)dx =(1/3) +∫_0 ^1   (f(x^2 ))^2 dx
$${determine}\:{f}\:\in{C}^{\mathrm{0}} \left(\left[\mathrm{0},\mathrm{1}\right],{R}\right)\:{verifying} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:=\frac{\mathrm{1}}{\mathrm{3}}\:+\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\left({f}\left({x}^{\mathrm{2}} \right)\right)^{\mathrm{2}} {dx} \\ $$

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