OpenStudy (anonymous):

challenging integral

2 years ago
OpenStudy (anonymous):

\[\int\limits_{0}^{\infty}\sin(x^2)\]

2 years ago
OpenStudy (anonymous):

Witha dx at the end ofc

2 years ago
OpenStudy (anonymous):

did you use a contour integral?

2 years ago
OpenStudy (anonymous):

@SithsAndGiggles ?

2 years ago
zepdrix (zepdrix):

\[\Large\rm \int\limits_0^{\infty}\sin(x^2)dx\quad=\quad \text{Im}\left(\int\limits_0^{\infty}e^{i x^2}dx\right)\]Looks like the error function kinda :) Hmm interesting problem.

2 years ago
OpenStudy (anonymous):

@satellite73 not exactly, I'm not sure how to set it up properly for lack of doing any complex analysis for a few months now. I mostly used Euler's formula at the time, like zepdrix wrote here.

2 years ago
zepdrix (zepdrix):

Oh your link didn't work when I first clicked it >.< Ah now I see.

2 years ago
OpenStudy (anonymous):

oh i see from the link and apparently you need to know \[\Gamma(\frac{1}{2})\]

2 years ago
OpenStudy (anonymous):

There's also a link to a page on MSE that uses real methods, which is a pretty neat approach.

2 years ago
OpenStudy (anonymous):

Laplace transform, by the looks of it!

2 years ago
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