Let for some function y = f(x), ${\int }_0^{\mathrm{x}} \mathrm{t}f\left(\mathrm{t}\right)\mathrm{dt}={\mathrm{x}}^2\mathrm{f}\left(\mathrm{x}\right),$ x > 0 and f(2) = 3. Then f(6) is equal to :

$\begin{array}{l}{\int }_0^{\mathrm{x}} \mathrm{tf}\left(\mathrm{t}\right)\mathrm{dt}={\mathrm{x}}^{2}f\left(\mathrm{x}\right),\mathrm{x}>0\\ \text{ Diff. both side w.r. to }x\\ xf\left(x\right)=x^2{f}^{\prime }\left(x\right)+2xf\left(x\right)\\ -xf\left(x\right)=x^2{f}^{\prime }\left(x\right)\\ \int \frac{f^{\prime }\left(x\right)}{f\left(x\right)}dx=\int \frac{-1}{2}dx\\ \log df\left(x\right)=-\log x+\log c\\ f\left(x\right)=\frac{c}{x}\begin{array}{} \end{array}\\ \mathrm{f}\left(2\right)=3\Rightarrow 3=\frac{\mathrm{c}}{2}\Rightarrow \mathrm{c}=6\\ f\left(x\right)=\frac{6}{x}\\ f\left(6\right)=1\end{array}$