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  4. The area of the figure bounded by the parabola x=-2 y2, x=1-3 y2 is

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Q. The area of the figure bounded by the parabola $x=-2 y^{2}, x=1-3 y^{2}$ is

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Solution:

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$A=\int\limits_{-1}^{1}\left(1-3 y^{2}\right)-\left(-2 y^{2}\right) d y$
$\Rightarrow A=2 \int\limits_{0}^{1}\left(1-y^{2}\right) d y=\frac{4}{3}$