MathematicsMedium38×since 2002Q3548Let the solution curve y=f(x)y=f(x)y=f(x) of the differential equation dydx+xyx2−1=x4+2x1−x2\frac{d y}{d x}+\frac{x y}{x^{2}-1}=\frac{x^{4}+2 x}{\sqrt{1-x^{2}}}dxdy+x2−1xy=1−x2x4+2x, x∈(−1,1)x\in(-1,1)x∈(−1,1) pass through the origin. Then ∫−3232f(x)dx\int\limits_{-\frac{\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}} f(x) d x−23∫23f(x)dx is equal toAπ3−14\frac{\pi}{3}-\frac{1}{4}3π−41Bπ3−34\frac{\pi}{3}-\frac{\sqrt{3}}{4}3π−43Cπ6−34\frac{\pi}{6}-\frac{\sqrt{3}}{4}6π−43Dπ6−32\frac{\pi}{6}-\frac{\sqrt{3}}{2}6π−23Check answerSkip