The area (in square units) of the region bounded by the curves $3y^2 = ax, y = a, a > 0$ and y-axis is:

$a^2$

The correct answer is Option (4) → $a^2$

Region: $x=\frac{3}{a}y^{2},\;y=a,\;x=0,\;y\ge0$

Area $= \displaystyle\int_{0}^{a}\left(\frac{3}{a}y^{2}-0\right)\,dy$

$=\frac{3}{a}\int_{0}^{a}y^{2}\,dy=\frac{3}{a}\left[\frac{y^{3}}{3}\right]_{0}^{a}=\frac{3}{a}\cdot\frac{a^{3}}{3}=a^{2}$