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Q.
Find the area bounded by the curve $x = 2 - y - y^2$ and y-axis.
Application of Integrals
Solution:
Put $2 - y - y^2 = 0$
$\Rightarrow y = 1, - 2$
This means, the curve intersects the y-axis at $y = 1$ and $y = - 2$.
Hence required area $= \int\limits^{1}_{-2} xdy$
$= \int\limits^{1}_{-2} \left(2-y-y^{2}\right)dy$
$= \left[2y-\frac{y^{2}}{2}-\frac{y^{3}}{3}\right]^{1}_{-2} = \frac{9}{2}$ sq. units
