Question

challenging integral

Answer 1

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

Answer 2

Witha dx at the end ofc

Answer 3

http://openstudy.com/users/sithsandgiggles#/updates/54a6df70e4b0a96030d869f4

Answer 4

http://www.wolframalpha.com/input/?i=integral+0+to+infinity++sin%28x^2%29

Answer 5

did you use a contour integral?

Answer 6

@SithsAndGiggles ?

Answer 7

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

Answer 8

@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.

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Laplace transform, by the looks of it!