The area of the region $\left{(\mathrm{x},\mathrm{y}):{\mathrm{x}}^{2}+4\mathrm{x}+2\leq \mathrm{y}\leq |\mathrm{x}+2|\right}$ is equal to [JEE Main 2025, 24 Jan (Shift 1)]

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The area of the region \(\left{(\mathrm{x},\mathrm{y}):{\mathrm{x}}^{2}+4\mathrm{x}+2\leq \mathrm{y}\leq |\mathrm{x}+2|\…

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