Question

Use the stationary phase approximation to get the leading-order (α to infty) asymptotics of the following integrals:
a) (1/π int₀π dt cos[α(ssin t - t)])
b) (int₀¹ dt eiα t)
a) (O(α-1/2))
b) (O(α-3/2))
c) (O(α-1))
d) (O(α-2))