Question:medium
Let \(y = y(x)\) be the solution of the differential equation \(x\sqrt{1-x^2} \, dy + (y\sqrt{1-x^2} - x \cos^{-1} x) \, dx = 0\), \(x \in (0, 1)\), \(\lim_{x \to 1^-} y(x) = 1\). Then \(y\left(\frac{1}{2}\right)\) equals:
Let \(y = y(x)\) be the solution of the differential equation \(x\sqrt{1-x^2} \, dy + (y\sqrt{1-x^2} - x \cos^{-1} x) \, dx = 0\), \(x \in (0, 1)\), \(\lim_{x \to 1^-} y(x) = 1\). Then \(y\left(\frac{1}{2}\right)\) equals:
Updated On: Apr 12, 2026
- \(3 - \frac{\pi}{\sqrt{3}}\)
- \(4 - \sqrt{3} \pi\)
- \(4 - \frac{2\pi}{\sqrt{3}}\)
- \(3 - \frac{\pi}{2\sqrt{3}}\)
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Integral Calculus
- The value of the integral $\int_0^\infty \frac{\log_e (x)}{x^2 + 4} dx$ is:
- JEE Main - 2026
- Mathematics
- Integral Calculus
- If \[ \alpha=\int_{0}^{2\sqrt{3}} \log_2(x^2+4)\,dx + \int_{2}^{4} \sqrt{2^x-4}\,dx, \] then \(\alpha^2\) is equal to _____.
- JEE Main - 2026
- Mathematics
- Integral Calculus
- If $\int_{-2}^2 ([\sin x] + |x \sin x|) dx = 2 \sin 2 - 4 \cos 2 - \beta$, then the value of $|\beta|$ where $[\cdot]$ is GIF is
- JEE Main - 2026
- Mathematics
- Integral Calculus
- If \( I(x) = \int \frac{16x+24}{x^2+2x-15}\,dx \), \( I(1) = 14\ln 3 \) and \( I(7) = \ln\left(2^\alpha \cdot 3^\beta\right) \), then \( (\alpha+\beta) \) is equal to
- JEE Main - 2026
- Mathematics
- Integral Calculus
- Want to practice more? Try solving extra ecology questions todayView All Questions
