Question

Area bounded by the curves $y=x^2$ and $y=2-x^2$ is

• A. $\frac{8}{3}$ sq. units
• B. $\frac{3}{8}$ sq. units
• C. $\frac{3}{2}$sq. units
• D. None of these

Answer 1

The correct option is A $\frac{8}{3}$ sq. units

Required area$=2$ Area of curve $OABO$
${\int }_0^t\left[\right(2-x^2)-(x^2\left)\right]dx={\int }_0^t\left[\right(2-2x^2\left)\right]dx$
$=4{[x-\frac{x^3}{3}]}_0^1=\frac{8}{3}$ sq.units