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.