JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\{(x, y) : 0 \leq y \leq 6 - x, y^2 \geq 4x - 3, x \geq 0\}\) is:
- A \(8\)
- B \(9\)
- C \(12\)
- D \(15\)
Answer & Solution
Correct Answer
(B) \(9\)
Step-by-step Solution
Detailed explanation
The given region is defined by the inequalities: \(x \geq 0\) \(0 \leq y \leq 6 - x \Rightarrow y \geq 0\) and \(x \leq 6 - y\) \(y^2 \geq 4x - 3 \Rightarrow x \leq \dfrac{y^2 + 3}{4}\) From these inequalities, for a given \(y \geq 0\), the value of \(x\) ranges from \(0\) to…
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