Mathematics - Area Under Curves Question with Solution | TestHub

$f(x)+f(y)\le 0⟺(x+3{)}^2+(y+3{)}^2\le 16$ : the disk of radius 4 centred at (-3, -3). Also $f(x)-f(y)=(x-y)(x+y+6)\le 0$ : the region between the lines $x=y$ and $x+y+6=0$, both of which pass through the centre (-3, -3). The two conditions together select exactly half the disk, so the area is $\frac{1}{2}\pi (4{)}^2=8\pi$.