Question

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

• A. $2units$
• B. $9/4units$
• C. $7/3units$
• D. $3units$

Answer 1

The correct option is B $9/4units$

$\Rightarrow$ Let $AB$ represents the line $y=3$ and $BOC$ represent the curve $y^2=4x$

$\Rightarrow$ We have to find area of shaded region.

$\Rightarrow$ Area of shaded region = Area of $AOB$

$={\int }_0^{3}xdy$

$\Rightarrow$ We know that, $y^2=4x$, so $x=\frac{y^2}{4}$

$\Rightarrow$ Area of shaded region $={\int }_0^{3}xdy$

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

$=\frac{1}{4}{\int }_0^3{y}^{2}dy$

$=\frac{1}{4}{\left[\frac{y^3}{3}\right]}_0^3$

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

$=\frac{1}{4}\times \frac{27}{3}$

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