JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region \(\{(x, y): y \leq \pi - |x|, y \leq |x \sin x|, y \geq 0\}\) is:
- A \(1 + \dfrac{\pi^2}{8}\)
- B \(2 + \dfrac{\pi^2}{4}\)
- C \(\dfrac{\pi^2}{8} - 1\)
- D \(4 + \dfrac{\pi^2}{2}\)
Answer & Solution
Correct Answer
(B) \(2 + \dfrac{\pi^2}{4}\)
Step-by-step Solution
Detailed explanation
The given region is defined by the inequalities \(y \leq \pi - |x|\), \(y \leq |x \sin x|\), and \(y \geq 0\). Since replacing \(x\) with \(-x\) leaves the inequalities unchanged, the region is symmetric with respect to the y-axis. We can find the area of the region in the first…
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