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determine-all-functions-f-C-0-R-R-0-x-f-x-dx-2-3-xf-x-




Question Number 50410 by Abdo msup. last updated on 16/Dec/18
determine all functions f ∈C^0 (R,R) /  ∫_0 ^x f(x)dx =(2/3)xf(x) .
$${determine}\:{all}\:{functions}\:{f}\:\in{C}^{\mathrm{0}} \left({R},{R}\right)\:/ \\ $$$$\int_{\mathrm{0}} ^{{x}} {f}\left({x}\right){dx}\:=\frac{\mathrm{2}}{\mathrm{3}}{xf}\left({x}\right)\:. \\ $$

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