The area of the region:

Question:

The area of the region:

$R=\left\{(x, y): 5 x^{2} \leq y \leq 2 x^{2}+9\right\}$ is :

 

  1. $11 \sqrt{3}$ square units

  2. $12 \sqrt{3}$ square units

  3. $9 \sqrt{3}$ square units

  4. $6 \sqrt{3}$ square units


Correct Option: , 2

Solution:

Required area $=2 \int_{0}^{\sqrt{3}}\left(2 x^{2}+9-5 x^{2}\right) d x$

$=2\left[9 x-x^{3}\right]_{0}^{\sqrt{3}}$

$=2[9 \sqrt{3}-3 \sqrt{3}]=12 \sqrt{3}$

 

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