JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Area Under Curves

The ellipse is $\frac{x^2}{4}+y^2=1$, with $a=2$ and $b=1$, so its area is $\pi ab=2\pi$. The lines $y=|x|-1$ and $y=1-|x|$ enclose a square with vertices $(\pm 1,0)$ and $(0,\pm 1)$, whose diagonals both have length $2$, giving area $\frac{1}{2}\cdot 2\cdot 2=2$. This square lies entirely inside the ellipse, so the area inside the ellipse and outside it is $2\pi -2=2(\pi -1)$.