The area of the region included between the regions satisfying and is

MATHEMATICS · Single correct · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles

Problem

The area of the region included between the regions satisfying min⁡(∣x∣,∣y∣)≥1\min(|x|, |y|) \ge 1 and x2+y2≤5x^2 + y^2 \le 5 is (1) 52(sin⁡−125−sin⁡−115)−4\frac{5}{2} \left( \sin^{-1} \frac{2}{\sqrt{5}} - \sin^{-1} \frac{1}{\sqrt{5}} \right) - 4 (2) 10(sin⁡−125−sin⁡−115)−410 \left( \sin^{-1} \frac{2}{\sqrt{5}} - \sin^{-1} \frac{1}{\sqrt{5}} \right) - 4 (3) 25(sin⁡−125−sin⁡−115)−4\frac{2}{5} \left( \sin^{-1} \frac{2}{\sqrt{5}} - \sin^{-1} \frac{1}{\sqrt{5}} \right) - 4 (4) 15(sin⁡−125−sin⁡−115)−415 \left( \sin^{-1} \frac{2}{\sqrt{5}} - \sin^{-1} \frac{1}{\sqrt{5}} \right) - 4

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