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Estimating complex integral

  1. Oct 1, 2011 #1
    1. The problem statement, all variables and given/known data
    I need to establish the estimate and inequality
    [itex]|\int_{C} e^{iz^{2}}dz| \leq\frac{\pi(1-e^{-R^{2}}}{4R} < \frac {\pi}{4R}[/itex]

    where [itex]C={z(t)=Re^{it},t\in[0,\fraq{\pi}{4}][/itex]
    2. Relevant equations

    3. The attempt at a solution
    I thought perhaps I could use the ML equality but the function doesn't have a global maximum. It does have a bound of 1 and -1 on the real and imaginary parts but using that as the maximum and then multiplying by the length does not give the inequality above.
    I'm at a loss on how to do anything with this question. It's quite frustrating.
  2. jcsd
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