The area (in sq. units) of the region enclose | vedclass

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Question

$y=x^{2}-1$ and $y=1-x^{2}$

$A=\int_{-1}^{1}\left(\left(1-x^{2}\right)-\left(x^{2}-1\right)\right) d x$

$A=\int_{-1}^{1}\left(2-2 x^{2}\right) d

Vedclass · Accepted Answer

$\frac{8}{3}$

Vedclass · Answer

$y=x^{2}-1$ and $y=1-x^{2}$

$A=\int_{-1}^{1}\left(\left(1-x^{2}\right)-\left(x^{2}-1\right)\right) d x$

$A=\int_{-1}^{1}\left(2-2 x^{2}\right) d x=4 \int_{0}^{1}\left(1-x^{2}\right) d x$

$A=4\left(x-\frac{x^{3}}{3}\right)_{0}^{1}=4\left(\frac{2}{3}\right)=\frac{8}{3}$

The area (in sq. units) of the region enclosed by the curves $y=x^{2}-1$ and $y=1-x^{2}$ is equal to

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