Let the area of the region \ (x, y): 2 y leq x 2 +3 . , y+ x leq 3, y geq x-1 \ be A. Then 6 A is equal to:

Mathematics · Area under the Curves

JEE Main 2025 — 29 January, Morning Shift — Question 51

Let the area of the region $\left\{(x, y): 2 y \leq x^{2}+3\right.$ , $y+|x| \leq 3, y \geq|x-1|\}$ be A. Then $6 A$ is equal to:

$A \Rightarrow$ Rectangle ABDE - Area of region EDC

\begin{aligned} & A \Rightarrow 4-2 \int_{0}^{1}(3-x)-\left(\frac{x^{2}+3}{2}\right) d x \\ & A \Rightarrow 4-2\left\{3 x-\frac{x^{2}}{2}-\frac{x^{3}}{6}-\frac{3}{2} x\right\}_{0}^{1} \end{aligned}

A \Rightarrow 4-2\left\{3-\frac{1}{2}-\frac{1}{6}-\frac{3}{2}\right\}=\frac{7}{3}

So $6 \mathrm{~A}=14$

Answer key and solution verified before publishing.

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