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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?

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    Inside an integral, $x$ is $x^2$. Just change variables, but be careful.2012-08-01

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