Find the area bounded by the curve `y^2=4a x` and the lines `y=2\ a n d\ ` y-axis.

Explanation

We have to find an area enclosed by curve `y^{2}=4 a x`, line `y=2 a` and `y` axis.

Thus, Required area


`=int_{0}^{2 a} x d y=int_{0}^{2 a} frac{y^{2}}{4 a} d y `

`=frac{1}{4 a}[frac{y^{3}}{3}]_{0}^{2 a}=frac{1}{12 a}[8 a^{3}-0] `

`=frac{2 a^{2}}{3} text { sq. unit. }`