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  4. The area of the region: R= (x, y): 5 x2 ≤ y ≤ 2 x2+9 is

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Q. The area of the region :
$R=\left\{(x, y): 5 x^{2} \leq y \leq 2 x^{2}+9\right\}$ is

JEE MainJEE Main 2021Application of Integrals

Solution:

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Required area $=2 \int_{0}^{\sqrt{3}}\left(2 x^{2}+9-5 x^{2}\right) d x$
$=2\left[9 x - x ^{3}\right]_{0}^{\sqrt{3}}$
$=2[9 \sqrt{3}-3 \sqrt{3}]=12 \sqrt{3}$