Integral of (cos^2 z) from ( - pi ) iota along |z|= pi to (pi) iota in the right half plane

STATE IF THE FUNCTION IS ANALYTIC OR NOT AND THEN INTEGRATE USING PARAMETRIC REPRESENTATION IF NOT ANALYTIC OR SIMPLY INTEGRATE using calculus IF ANALYTIC.

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- Apr 1st 2013, 02:58 AMszak1592Complex integration of cos^2 z, please help?
Integral of (cos^2 z) from ( - pi ) iota along |z|= pi to (pi) iota in the right half plane

STATE IF THE FUNCTION IS ANALYTIC OR NOT AND THEN INTEGRATE USING PARAMETRIC REPRESENTATION IF NOT ANALYTIC OR SIMPLY INTEGRATE using calculus IF ANALYTIC. - Apr 1st 2013, 09:57 AMSworDRe: Complex integration of cos^2 z, please help?
It is analytic, so just do

$\displaystyle \int_{-\pi}^{\pi} \cos^2(z) dz$

$\displaystyle =\int_{-\pi}^{\pi} \frac{1+\cos(2z)}{2} dz$

$\displaystyle =\frac{1}{2}z+\frac{1}{4}\sin(2z)$ from -Pi to Pi

$\displaystyle =\frac{\pi}{2} + \frac{\pi}{2} + 0 - 0 = \pi$