Area of the region bounded by the curve $y^2 = 4x$, y-axis and the line $y = 3$ is equal to

$\frac{9}{4}$ sq. units

The correct answer is Option (4) → $\frac{9}{4}$ sq. units

$y^{2}=4x\;\Rightarrow\;x=\frac{y^{2}}{4}$

$\text{Area}=\int_{0}^{3}\frac{y^{2}}{4}\,dy$

$=\frac{1}{4}\int_{0}^{3}y^{2}\,dy$

$=\frac{1}{4}\left(\frac{y^{3}}{3}\right)\Big|_{0}^{3}$

$=\frac{1}{4}\cdot\frac{27}{3}$

$=\frac{27}{12}$

$=\frac{9}{4}$

The required area of the region is $\frac{9}{4}$ square units.