Perturbative Methods for Modelling (M2)

Example 2, p. 283

Figure 6.6 p. 284

By deforming the integration path in the complex plane and using the Laplace's method, show that $\fs2 I(x) = \int_0^\infty e^{i\, x \, t^2} \,dt\sim {1\over 2} \sqrt{\pi \over x} \, e^{i\, \pi/4}$ for $\fs2 x\to +\infty$.