Estimating complex integral

  • Thread starter Brendy
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Homework Statement


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]

Homework Equations





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.
 

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