JEE Mains · Maths · STD 12 - 8. Application and integration
The area of the region described by \(A=\{(x,y):x^2 + y^2 \le 1\,and\,y^2 \le 1-x \}\) is
- A \(\frac{\pi }{2} - \frac{2}{3}\)
- B \(\frac{\pi }{2} + \frac{2}{3}\)
- C \(\frac{\pi }{2} + \frac{4}{3}\)
- D \(\;\frac{\pi }{2} - \frac{4}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi }{2} + \frac{4}{3}\)
Step-by-step Solution
Detailed explanation
\(A_{1}=2\left|\int_{0}^{1} \sqrt{1-x}\right| d x\) \(A_{1}=2\left|\int_{1}^{0} 2 t^{2} d t\right|\) \(A_{1}=4 \cdot \frac{1}{3}\) \(\boxed{Area = \frac{\pi }{2} + \frac{4}{3}}\)
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