Question

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

• A. $\frac{7}{2}$
• B. $\frac{4}{3}$
• C. $\frac{16}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is D $\frac{8}{3}$

Total area = $4{\int }_0^1(1-x^2)dx=4{[x-\frac{x^3}{3}]}_0^1$
$=4[1-\frac{1}{3}]=\frac{8}{3}sq.unit$