Question Number 205826 by tri26112004 last updated on 31/Mar/24
![f_([0;3]) (x)>0 f(0)=3 f(3)=8 ∫^3 _0 (([f′(x)]^2 )/(f(x)+1))dx = (4/3) f(2)=¿](https://www.tinkutara.com/question/Q205826.png)
$$\underset{\left[\mathrm{0};\mathrm{3}\right]} {{f}}\left({x}\right)>\mathrm{0} \\ $$$${f}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{8} \\ $$$$\underset{\mathrm{0}} {\int}^{\mathrm{3}} \frac{\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{{f}\left({x}\right)+\mathrm{1}}{dx}\:=\:\frac{\mathrm{4}}{\mathrm{3}} \\ $$$${f}\left(\mathrm{2}\right)=¿ \\ $$