Question

The area bounded by the curve $x=3y^2-9$ and the line $x=0$, $y=0$ and $y=1$ is

• A. $8$ sq. units
• B. $8/3$ sq. units
• C. $3/8$ sq. units
• D. $3$ sq. units

Answer 1

Answer: (A)

We have, $x=3y^2-9\Rightarrow 3y^2=x+9$

Required area = area of shaded region
$A=\left|\underset{0}{\overset{1}{\int }}\left(3y^2-9\right)dy\right|={\left|y^3-9y\right|}_0^1=\left|1-9\right|=8$ sq. units