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Homework Help: Deriving Fresnel Integrals

  1. Mar 5, 2008 #1
    The problem statement, all variables and given/known data
    Integrate [itex]e^{iz^2}[/itex] around the contour C to obtain the Fresnel integrals:

    [tex]\int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4}[/tex]

    The contour consists of three parts:

    1. z = x, [itex]0 \le x \le R[/itex]
    2. z = [itex]Re^{i\theta}[/itex], [itex]0 \le \theta \le \pi/4[/itex]
    3. z = [itex]te^{i\pi/4}[/itex], [itex] R \ge t \ge 0[/itex]

    The attempt at a solution
    I'm stumped because I don't know how to evaluate integrals of the form [itex]e^{iz^2}[/itex]. How would I do this?
  2. jcsd
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