Evaluate the following Integral: ∫cos^-1(cos x)dx, x ∈ [0, 2π]

Question

Evaluate the following Integral:

\(\int\limits_{0}^{2\pi} \)cos^-1(cos x)dx

Answer 1

 \(\int\limits_{0}^{2\pi} \)cos^-1(cos x)dx

= \(-\int\limits_{0}^{\pi} \)cos^-1(cos x) dx + \(\int\limits_{\pi}^{2\pi} \)cos^-1(cos x) dx 

= \(-\int\limits_{0}^{\pi} \)x dx + \(\int\limits_{\pi}^{2\pi} \)x dx