Question

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

• A. $\frac{9}{4}$
• B. $\frac{3}{4}$
• C. $\frac{2}{3}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{9}{4}$

Required area = Area of OAB = ${\int }_0^{3}xdy$

$={\int }_0^3\frac{y^2}{4}dy$

$=\frac{1}{4}{\left[\frac{y^3}{3}\right]}_0^3=\frac{1}{12}\times 27=\frac{9}{4}$ units