Documents Stein and Shak Arch i Complex Analysis So Ln

Chapter 2.6, Page 64 Exercise 1: Prove that _ ∞ 0 sin(x 2 )dx = _ ∞ 0 cos(x 2 )dx = √ 2π 4 . These are the Fresnel integrals. Here, _ ∞ 0 is interpreted as lim R→∞…