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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Mathematics
Chapter
Area Under Curves

BITSAT 2023 · Paper 2 · Mathematics · Area Under Curves

The area of the region R=\ (x, y): 5 x^2 ≤ y ≤ 2 x^2+9\ is :

The area of the regionR={(x,y):5x2≤y≤2x2+9} is  : \mathbf{R}=\left\{(x, y): 5 x^2 \leq y \leq 2 x^2+9\right\} \text{\text{ is } : }

Options

  1. A11311 \sqrt{3} square units
  2. B12312 \sqrt{3} square units
  3. C939 \sqrt{3} square units
  4. D636 \sqrt{3} square units

Correct answer

B. 12312 \sqrt{3} square units

Step-by-step solution

 Required area =2∫03(2x2+9−5x2)dx=2[9x−x3]03=2[93−33]=123.\begin{aligned} & \text{ Required area }=2 \int_0^{\sqrt{3}}\left(2 x^2+9-5 x^2\right) d x \\ & =2\left[9 x-x^3\right]_0^{\sqrt{3}}=2[9 \sqrt{3}-3 \sqrt{3}]=12 \sqrt{3}.\end{aligned}
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