JEE MAIN - Mathematics (2025 - 3rd April Morning Shift - No. 24)
The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, the $x$-axis and the lines $x=-2$ and $x=4$ is equal to__________
Answer
12
Explanation
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Area =
$$\begin{aligned} & \frac{1}{2} \times 2 \times 2+\int_0^1\left(2 x-x^2\right) d x+\int_1^3 x d x+\int_3^4\left(x^2-2 x\right) d x \\ & =2+\left[\frac{2 x^2}{2}-\frac{x^3}{3}\right]_0^1+\left[\frac{x^2}{2}\right]_1^3+\left[\frac{x^3}{3}-\frac{2 x^2}{2}\right]_3^4 \end{aligned}$$
= 12 square units
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