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Numerically it seems to be true that

$$ \int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}. $$

Any ideas how to prove this?

  • 3
    Substitute $u=\sqrt{x}$ to see that this is related to [Fresnel's integral](http://en.wikipedia.org/wiki/Fresnel_integral#Properties)...2012-07-17

6 Answers 6