Question

Choose the correct answer in the following.

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

(a) $2$ (b) $\frac{9}{4}$

(c) $\frac{9}{3}$ (d) $\frac{9}{2}$

Answer 1

The area bounded by the curve, $y^2=4x,$ Y - axis and y = 3 is represented in the figure by shaded region.

Required area $={\int }_0^3|x|dy$

$={\int }_0^3\frac{y^2}{4}dy=\frac{1}{4}[\frac{y^3}{3}{]}_0^3=\frac{1}{12}(3^3-0)=\frac{1}{12}(27)$

$=\frac{9}{4}sq$ unit. Thus, the correct option is (b).