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Q.
The area of the domain of the function $f(x, y)=\sqrt{16-x^2-y^2}-\sqrt{|x|-y}$ is $k \pi$ where $k$ equals
Application of Integrals
Solution:
From the first radical sign
$x^2+y^2 \leq 16$ i.e. interior of a circle with circle $(0,0)$ and radius 4 .
From the $2^{\text {nd }}$ radical sign $y \leq|x|$
i.e. $ \frac{3}{4}$ th of the circle
$\therefore $ Required area $=(\pi \cdot 16) \frac{3}{4}=12 \pi$.
