Question

${\int }_0^{\pi }\frac{dx}{1+3^{\cos x}}$is equal to

• A. $-\pi$
• B. $0$
• C. $\frac{\pi }{2}$
• D. none of these

Answer 1

Answer: (C)

$\frac{\pi }{2}$

Let, $I={\int }_0^{\pi }\frac{dx}{1+3^{\cos x}}$ ..(1)
Using above formula,
$I={\int }_0^{\pi }\frac{dx}{1+3^{\cos (\pi -x)}}={\int }_0^{\pi }\frac{3^{\cos x}dx}{1+3^{\cos x}}$ ..(2)
Adding (1) and (2) we get,
$I=\frac{1}{2}{\int }_0^{\pi }dx=\frac{\pi }{2}$