JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(S=\left\{(x, y): 3 x^{2} \leq 4 y \leq 6 x+24\right\} \text { is }...... \,.\)
- A \(66\)
- B \(12\)
- C \(27\)
- D \(99\)
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
For \(A \,\&\, B\) \(3 x^{2}=6 x+24 \Rightarrow x^{2}-2 x-8=0\) \(\Rightarrow x=-2,4\) \(\text { Area }=\int_{-2}^{4}\left(\frac{3}{2} x+6-\frac{3}{4} x^{2}\right) \,d x\) \(=\left[\frac{3 x^{2}}{4}+6 x-\frac{x^{3}}{4}\right]_{-2}^{4}=27\)
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