Question

Evaluate the integral
${\int }_0^{\pi }\frac{\cos x}{1+{\sin }^{2}x}dx$

• A. $\frac{\pi }{4}$
• B. $0$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is B $0$

${\int }_0^{a}f\left(x\right)dx={\int }_0^{a}f(a-x)dx$
$\Rightarrow I={\int }_0^{\pi }\frac{cosx}{1+si{n}^{2}x}dx$ ---(1)
$\Rightarrow I={\int }_0^{\pi }\frac{-cosx}{1+si{n}^{2}x}dx$ ---(2)

Adding 1 + 2, we get

$\Rightarrow 2I=0$

$\therefore I=0$