The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, then $x$-axis and the lines $x=-2$ and $x=4$ is equal to _______ .

Solution

$\begin{aligned} & \text { Required Area }=\frac{1}{2} \times 2 \times 2+\frac{1}{2} \times 3 \times 3+\frac{1}{2} \times 1 \times 11 \\ & =12\end{aligned}$

Hence, the correct answer is 12.