Prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \sqrt{\frac{\pi}{8}}$ Further prove that: $\displaystyle \int_0^{\infty}\sin(x^2)\,dx = \int_0^{\infty}\cos(x^2)\,dx$ Help on either one would be much appreciated.
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Fresnel integral - Wikipedia, the free encyclopedia
Oh, so I imagine this is tough to prove. This isn't a homework problem or anything; I just found it by accident while using Maple and was curious why it was true.
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