Verified Solution • 2025–26 Session moderate

QJEEM25Ma9f58: JEE Main 2025 Mathematics - Class 12 JEEM25Ma9f58 Solution: The area (in sq. units) of the region is

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

Multiple Choice Options

  • A 323\frac{32}{3}
  • B 643\frac{64}{3}
  • C 173\frac{17}{3}
  • D 803\frac{80}{3}

Step-by-Step Verified Solution

JEE Main 2025 (Online) 28th January Morning Shift Mathematics - Area Under The Curves Question 1 English Explanation

amp; Area =2[∫02(x2+1)dx+∫23(2x+1)dx]amp;⇒643∴(2)\begin{aligned}& \text { Area }=2\left[\int_0^2\left(\mathrm{x}^2+1\right) \mathrm{dx}+\int_2^3(2 \mathrm{x}+1) \mathrm{dx}\right] \\& \Rightarrow \frac{64}{3} \quad \therefore(2)\end{aligned}

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