1.The function y=f(x)y = f(x)y=f(x) is the solution of dydx+xyx2−1=x4+2x1−x2\frac{dy}{dx} + \frac{xy}{x^2-1} = \frac{x^4+2x}{\sqrt{1-x^2}}dxdy+x2−1xy=1−x2x4+2x in (−1,1)(-1,1)(−1,1) satisfying f(0)=0f(0)=0f(0)=0. Then ∫−3/23/2f(x) dx\int_{-\sqrt{3}/2}^{\sqrt{3}/2} f(x)\,dx∫−3/23/2f(x)dx isa.π3−32\frac{\pi}{3} - \frac{\sqrt{3}}{2}3π−23b.π3−34\frac{\pi}{3} - \frac{\sqrt{3}}{4}3π−43c.π6−34\frac{\pi}{6} - \frac{\sqrt{3}}{4}6π−43d.π6−32\frac{\pi}{6} - \frac{\sqrt{3}}{2}6π−23Login to continueOnly logged in users canattempt or see the solution.
