The area (in sq. units) of the region described by $A=\left\{(x, y): x^2+y^2 \leq 1 ext { and } y^2 \leq 1-x ight\}$ is

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The area (in sq. units) of the region described by $A=\left\{(x, y): x^2+y^2 \leq 1 	ext { and } y^2 \leq 1-xight\}$ is

Aicharya · Accepted Answer

$\begin{aligned} & A=\left\{(x, y): x^2+y^2 \leq 1 	ext { and } y^2 \leq 1-xight\} \ & =	ext { Area of semicircle }+ 	ext { Area of the region bounded by parabola and } \ & 	ext { y-axis } \ & =\frac{\pi 	imes 1^2}{2}+2 \int_0^1 \sqrt{1-x} d x \ & =\frac{\pi}{2}+2 	imes \frac{2}{3}\left[-(1-x)^{3 / 2}ight]_0^1 \ & =\frac{\pi}{2}+\frac{4}{3}\left[-0^{3 / 2}+1^{3 / 2}ight] \ & =\frac{\pi}{2}+\frac{4}{3}\end{aligned}$

The area (in sq. units) of the region described by $A=\left\{(x, y): x^2+y^2 \leq 1 \text { and } y^2 \leq…

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