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JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region : \(R =\left\{( x , y ): 5 x ^{2} \leq y \leq 2 x ^{2}+9\right\}\) is ........ \(square\, units\)
- A \(11 \sqrt{3}\)
- B \(12 \sqrt{3}\)
- C \(9 \sqrt{3}\)
- D \(6 \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(12 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
Required area \(=2 \int_{0}^{\sqrt{3}}\left(2 x ^{2}+9-5 x ^{2}\right) dx\) \(=2\left[9 x - x ^{3}\right]_{0}^{\sqrt{3}}\) \(=2[9 \sqrt{3}-3 \sqrt{3}]=12 \sqrt{3}\)
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