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Q.
The area bounded by the curve $x = 3y^{2} - 9$ and the line $x = 0$, $y = 0$ and $y = 1$ is
Application of Integrals
Solution:
We have, $x=3y^{2}-9 \,\Rightarrow \quad3y^{2}=x+9$
Required area = area of shaded region
$A=\left|\int\limits_{0}^{1}\left(3y^{2}-9\right)dy\right|=\left|y^{3}-9y\right|_{0}^{1}=\left|1-9\right|=8$ sq. units
