Solve this following


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


  1. $\frac{4}{3}$

  2. $\frac{8}{3}$

  3. $\frac{16}{3}$

  4. $\frac{7}{2}$

Correct Option:


$y=x^{2}-1$ and $y=1-x^{2}$

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

$A=\int_{-1}^{1}\left(2-2 x^{2}\right) d x=4 \int_{0}^{1}\left(1-x^{2}\right) d x$



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