The area (in sq. units) of the region \ ( x , y ): 0 leq y leq 2 x +1,0 leq y leq x 2 +1, x leq 3 \ is

Mathematics · Area under the Curves

JEE Main 2025 — 28 January, Morning Shift — Question 20

The area (in sq. units) of the region $\left\{(\mathrm{x}, \mathrm{y}): 0 \leq \mathrm{y} \leq 2|\mathrm{x}|+1,0 \leq \mathrm{y} \leq \mathrm{x}^{2}+1,|\mathrm{x}| \leq 3\right\}$ is

Option A:
$\frac{80}{3}$
Option B:
$\frac{64}{3}$
Correct
Option C:
$\frac{17}{3}$
Option D:
$\frac{32}{3}$

Answer: B

Step-by-step solution

Area $=2\left[\int_{0}^{2}\left(x^{2}+1\right) d x+\int_{2}^{3}(2 x+1) d x\right]$

$\Rightarrow \frac{64}{3}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 28 January, Morning Shift
Subject: Mathematics
Chapter: Area under the Curves
Topic: Area under the Curves