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  4. Area enclosed between the curves |y|=|1-x2| and x2+y2=1, is

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Q. Area enclosed between the curves $|y|=\left|1-x^2\right|$ and $x^2+y^2=1$, is

Application of Integrals

Solution:

image
$|y|=1-x^2, $
$C_1: x^2+y^2=1 $
$C_2: y=1-x^2 $
$C_3: y=x^2-1 $
$\text { Required area }=\pi-4 \Delta_1$
$=\pi-4 \int_0^1\left(1-x^2\right) d x$
$=\pi-\frac{8}{3}=\frac{3 \pi-8}{3}$