JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Area Under Curves

Let $t=x-1$; then $y=||t|-2|$. This is $0$ when $|t|=2$ (i.e. $x=-1$ and $x=3$), and equals $2-|x-1|$ for $|x-1|\le 2$, forming a tent over the x-axis with vertices $(-1,0),(1,2),(3,0)$. The bounded region enclosed between this curve and the x-axis is a triangle of base $4$ and height $2$: area $=\frac{1}{2}\times 4\times 2=4$.