Area of the region bounded by the curve

Question:

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

A. 2

B. $\frac{9}{4}$

C. $\frac{9}{3}$

D. $\frac{9}{2}$

Solution:

The area bounded by the curve, $y^{2}=4 x, y$-axis, and $y=3$ is represented as

$\therefore$ Area $\mathrm{OAB}=\int_{0}^{3} x d y$

$=\int_{0}^{3} \frac{y^{2}}{4} d y$

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

$=\frac{1}{12}(27)$

$=\frac{9}{4}$ units

Thus, the correct answer is B.