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  4. The area of the region given by A = ( x , y ): x 2 ≤ y ≤ min x +2,4-3 x is :

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Q. The area of the region given by $A =\left\{( x , y ): x ^2 \leq y \leq \min \{ x +2,4-3 x \}\right\}$ is :

JEE MainJEE Main 2022Application of Integrals

Solution:

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$A=\int\limits_{-1}^{\frac{1}{2}}\left(x+2-x^2\right) d x+\int\limits_{\frac{1}{2}}^1\left(4-3 x-x^2\right) d x=\frac{17}{6}$