Question

Area enclosed between the curves $|y|=1-x^2$ and $x^2+y^2=1$ is

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

Answer 1

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


The dotted area is
$A=\underset{0}{\overset{1}{\int }}(1-x^2)dx$
$={(x-\frac{x^3}{3})}_0^1$
$=1-\frac{1}{3}=\frac{2}{3}$

Hence, area bounded by circle $x^2+y^2=1$ and $|y|=1-x^2$
= Lined area
= Area of circle - Area bounded by $|y|=1-x^2$
$=\pi -4\times \left(\frac{2}{3}\right)=\frac{3\pi -8}{3}\text{sq. units}$