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