Question

Area of the region enclosed between the curves $x=y^2-1$ and $x=\left|y\right|\sqrt{1-y^2}$ is

• A. $1$
• B. $4/3$
• C. $2/3$
• D. $2$

Answer 1

The correct option is D $2$

Required area is,
$A=2{\int }_0^1[y\sqrt{1-y^2}-(y^2-1)]dy$
$={\left(\frac{-2}{3}{(1-y^2)}^{3/2}\right)}_0^1-{(\frac{2y^3}{3}-2y)}_0^1=2$