Practice problem
Evaluate: ∫0πxsinx1+cos2x dx\int_{0}^{\pi}\frac{x\sin x}{1+\cos^{2}x~}dx∫0π1+cos2x xsinxdx (Hint: try to prove ∫0πxf(sinx) dx=π∫0π2f(sinx) dx\int_{0}^{\pi}xf(\sin x)~dx=\pi\int_{0}^{\frac{\pi}{2}}f(\sin x)~dx∫0πxf(sinx) dx=π∫02πf(sinx) dx)
π\piπ
π23\dfrac{\pi^{2}}{3}3π2
7\sqrt{7}7
π24\dfrac{\pi^{2}}{4}4π2
26π2\dfrac{\sqrt{2}}{6}\pi^{2}62π2
Type a concept, like “slope” or “photosynthesis”.