# Homework Help: Deriving Fresnel Integrals

1. Mar 5, 2008

### e(ho0n3

The problem statement, all variables and given/known data
Integrate $e^{iz^2}$ around the contour C to obtain the Fresnel integrals:

$$\int_0^\infty \cos(x^2) \, dx = \int_0^\infty \sin(x^2) \, dx = \frac{\sqrt{2\pi}}{4}$$

The contour consists of three parts:

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

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