JEE MAIN - Mathematics (2025 - 28th January Morning Shift - No. 20)
The area (in sq. units) of the region $\left\{(x, \mathrm{y}): 0 \leq \mathrm{y} \leq 2|x|+1,0 \leq \mathrm{y} \leq x^2+1,|x| \leq 3\right\}$ is
$\frac{32}{3}$
$\frac{64}{3}$
$\frac{17}{3}$
$\frac{80}{3}$
Explanation
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$$\begin{aligned} & \text { Area }=2\left[\int_0^2\left(\mathrm{x}^2+1\right) \mathrm{dx}+\int_2^3(2 \mathrm{x}+1) \mathrm{dx}\right] \\ & \Rightarrow \frac{64}{3} \quad \therefore(2) \end{aligned}$$
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