JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region \(\left\{( x , y ): x ^{\frac{2}{3}}+ y ^{\frac{2}{3}} \leq 1 x + y \geq 0, y \geq 0\right\}\) is \(A\), then \(\frac{256 A }{\pi}\)
- A \(36\)
- B \(-36\)
- C \(66\)
- D \(-66\)
Answer & Solution
Correct Answer
(C) \(66\)
Step-by-step Solution
Detailed explanation
\(A =\frac{3}{2} \int\limits_{0}^{1}\left(1- x ^{2 / 3}\right)^{3 / 2} dx\) Let \(x=\sin ^{3} \theta\) \(A =\frac{3}{2} \int\limits_{0}^{\pi / 2}\left(1-\sin ^{2} \theta\right)^{3 / 2} \cdot 3 \sin ^{2} \theta \cos \theta d \theta\)…
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