QJEEM22Ma3427: JEE Main 2022 Mathematics - Class 12 JEEM22Ma3427 Solution: The area of the region given by is :

Question

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The area of the region given by

$A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}$ is :

Accepted Answer

A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right.

So area of required region

\begin{aligned}&amp;A=\int_{-1}^{\frac{1}{2}}\left(x+2-x^{2}\right) d x+\int_{\frac{1}{2}}^{1}\left(4-3 x-x^{2}\right) d x \\\\&amp;=\left[\frac{x^{2}}{2}+2 x-\frac{x^{3}}{3}\right]_{-1}^{\frac{1}{2}}+\left[4 x-\frac{3 x^{2}}{2}-\frac{x^{3}}{3}\right]_{\frac{1}{2}}^{1} \\\\&amp;=\left(\frac{1}{8}+1-\frac{1}{24}\right)-\left(\frac{1}{2}-2+\frac{1}{3}\right)+\left(4-\frac{3}{2}-\frac{1}{3}\right)-\left(2-\frac{3}{8}-\frac{1}{24}\right) \\\\&amp;=\frac{17}{6}\end{aligned}

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