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JEE Main 202528 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
28 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2025 · 28 January · Morning Shift · Mathematics · Area Under Curves

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

The area (in sq. units) of the region {(x,y):0≤y≤2∣x∣+1,0≤y≤x2+1,∣x∣≤3}\left\{(x, y): 0 \leq \mathrm{y} \leq 2|x|+1,0 \leq \mathrm{y} \leq x^2+1,|x| \leq 3\right\} is

Options

  1. A803\frac{80}{3}
  2. B643\frac{64}{3}
  3. C323\frac{32}{3}
  4. D173\frac{17}{3}

Correct answer

B. 643\frac{64}{3}

Step-by-step solution

 Area =2[∫02(x2+1)dx+12[5+7]×1]=643\begin{aligned} & \text{ Area }=2\left[\int_0^2\left(x^2+1\right) d x+\frac{1}{2}[5+7] \times 1\right] \\ & =\frac{64}{3}\end{aligned}
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