Doing complex analysis, I encountered a problem that I do not know how to solve. I am to prove the Fresnel integrals from $x = 0$ to infinity, using a contour integral of $e^{i x^2}$. The hint said to use Jordan's lemma, but that pertains to a function $e^{ix}$ times a function $G(x)$, but as far as I can tell there is no way to pick $G$ so that the total ends up as $e^{i x^2}$.
Does anyone know what to do?