Area bounded by the curve \(y^{2}(2a-x)=x^{3}\) and the line \(x=2a\) is

\(3\pi a^{2}\) \(3\pi \frac{a^{2}}{2}\) \(3\pi \frac{a^{2}}{4}\) None of these

None of these

\(\begin{aligned}\text{Area}&=2\int_{0}^{2a}ydx\\ &=2\int_{0}^{2a}\sqrt{\frac{x^{3}}{2a-x}}dx\\ &=6\pi a^2\end{aligned}\)