Question:medium
If \((x\sqrt{1-x^2}) \, dy - (y\sqrt{1-x^2} - x^2 \cos^{-1} x) \, dx = 0\) and \(\lim_{x \to 1^-} y(x) = 1\), then \(y\left(\frac{1}{2}\right)\) is
If \((x\sqrt{1-x^2}) \, dy - (y\sqrt{1-x^2} - x^2 \cos^{-1} x) \, dx = 0\) and \(\lim_{x \to 1^-} y(x) = 1\), then \(y\left(\frac{1}{2}\right)\) is
Updated On: Apr 9, 2026
- \(\frac{\pi^2}{36}\)
- \(\frac{\pi^2 + 18}{36}\)
- \(\frac{\pi^2 - 18}{36}\)
- \(\frac{\pi^2}{18}\)
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The Correct Option is B
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