# Homework Help: Method of stationary phase

1. Oct 24, 2011

### math2011

1. The problem statement, all variables and given/known data

Find asymptotic expansions for the following integral, as $x \to \infty$, using the method of stationary phase.

$$\int^1_0 e^{ixt^p} dt, p > 1$$

2. Relevant equations

3. The attempt at a solution

1. let the phase be $t^2$. is this correct?
2. $\frac{d}{dt} t^2 = 2t = 0$, so phase stationary is $0$.
3. expand phase about stationary point $t=0$ and i get $0$. something is wrong, should i be doing this?