# Linked Questions

10 questions linked to/from Some way to integrate $\sin(x^2)$?
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### Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?

I have seen the Fresnel integral $$\int_0^\infty \sin x^2\, dx = \sqrt{\frac{\pi}{8}}$$ evaluated by contour integration and other complex analysis methods, and I have found these methods to be the ...
6answers
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### Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.

$\sin x^2$ does not converge as $x \to \infty$, yet its integral from $0$ to $\infty$ does. I'm trying to understand why and would like some help in working towards a formal proof.
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### Historical context: The Fresnel integrals

The evaluation of the Fresnel integrals has been done a plethora of times both on this site, and numerous other places. The two main ways of evalutating these integrals has either been with some ...
1answer
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### Help on contour integral on another answer on this site

Do you mind expanding on the part along the diagonal in the first answer by Robjohn to this question proof? Particularly how to achieve (3). I am trying use a parameterization for $z=xe^{i \pi/4}$ ...