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Math Help - Complex integration of cos^2 z, please help?

  1. #1
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    Wah Cantt
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    Complex 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.
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  2. #2
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    Re: Complex integration of cos^2 z, please help?

    It is analytic, so just do
    \int_{-\pi}^{\pi} \cos^2(z) dz

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

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

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