Mathematics - Area Under Curves Question with Solution | TestHub

$|x+y|\le 2$ and $|x-y|\le 2$ give the square with vertices $(\pm 2,0),(0,\pm 2)$, of area 8. The ellipse $2x^2+6y^2=3$ has semi-axes $\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{1}{2}}$, lies inside the square, and has area $\pi \cdot \sqrt{\frac{3}{2}}\cdot \sqrt{\frac{1}{2}}=\frac{\pi \sqrt{3}}{2}$. Required area $=8-\frac{\pi \sqrt{3}}{2}$ sq. units.