Official solution
\[\& {y}^{2}\le 4x,x0 \ \& :y>0 \ \& \frac{x(x-1)(x-2)}{(x-3)(x-4)}>0 \ \& x\in (0,1)\cup (2,3) \ \& - \ \& \frac{x(x-1)(x-2)}{(x-3)(x-4)}\]
\[\begin{gathered} =2\int _{0}^{4}\sqrt{x}dx \\ =2\cdot \frac{2}{3}{[{x}^{3/2}]}_{4}^{0}=\frac{32}{3} \end{gathered}\]