$\int_0^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^2 x} d x$ has the value

Question

Aicharya · Accepted Answer

$\begin{aligned} & \int_0^{\pi / 2} \frac{\sin x}{1+\cos ^2 \mathrm{x}} \mathrm{dx}=-\int_1^0 \frac{\mathrm{dt}}{1+\mathrm{t}^2}[	ext { let } \cos \mathrm{x}=\mathrm{t}] \ & =-\left[	an ^{-1} \mathrm{t}ight]_1^0 \ & =-\left(0-\frac{\pi}{4}ight) \ & =\frac{\pi}{4}\end{aligned}$

$\int_0^{\frac{\pi}{2}} \frac{\sin x}{1+\cos ^2 x} d x$ has the value

Solution