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Questions Asked in Previous 10 Years' Exams
The function \( y=f(x) \) is the solution of the differential equation \( \frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\sqrt{1-x^{2}}} \) in \( (-1,1) \) satisfying \( f(0)=0 \). Then, \( \int_{-\frac{\sqrt{3}}{2}}^{\sqrt{3} / 2} f(x) d x \) is [Only One correct 2014]
(a) \( \frac{\pi}{3}-\frac{\sqrt{3}}{2} \)
(b) \( \frac{\pi}{3}-\frac{\sqrt{3}}{4} \)
(c) \( \frac{\pi}{6}-\frac{\sqrt{3}}{4} \)
(d) \( \frac{\pi}{6}-\frac{\sqrt{3}}{2} \).
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