Question

$\int_{\pi/4}^{3\pi/4}\frac{dx}{1 + cosx}$ is equal to

• A. 2
• B. –2
• C. $\frac{1}{2}$
• D. –$\frac{1}{2}$

Answer 1

Answer: (A)

2

Answer 2

Let I = $\int_{\pi/4}^{3\pi/4}\frac{dx}{1 + \cos x}$ = $\int_{\pi/4}^{3\pi/4}\frac{dx}{1 - \cos x}$

⇒ 2I = 2$\int_{\pi/4}^{3\pi/4}\frac{dx}{1 - \cos^{2}x}$

= 2$\int_{\pi/4}^{3\pi/4}{\cos ec^{2}xdx} = - \left. \ 2\cot x \right|_{\pi/4}^{3\pi/4} = 4$ ⇒ I = 2