Area of the region bounded by curve $y^2 = 4x$ and the X-axis between $x = 0$ and $x = 1$ is

$\frac{8}{3}$

The correct answer is Option (2) → $\frac{8}{3}$

Given

$\text{Required Area} = 2 \int_{0}^{1} y \, dx$

$= 2 \int_{0}^{1} 2\sqrt{x} \, dx$

$= 4 \int_{0}^{1} x^{\frac{1}{2}} \, dx$

$= 4 \left[ \frac{x^{\frac{3}{2}}}{\frac{3}{2}} \right]_{0}^{1}$

$= \frac{8}{3} \text{ sq. units}$