The integral is :(adsbygoogle = window.adsbygoogle || []).push({});

[PLAIN]http://i038.radikal.ru/1108/ed/a6cd0c5e8f36.jpg [Broken]

, where "y" - coordinate, "kx" - component of wave vector

if we calculate this integral on a paper with a pen and using compex variables theory we obtain:

1) y>0

here, in the capacity of contour we take semicircumference in the upper half plane

[URL]http://s006.radikal.ru/i215/1108/c9/835aa4a65f60.jpg[/URL]

2) y<0

here, in the capacity of contour we take semicircumference in the lower half plane

[URL]http://s58.radikal.ru/i162/1108/b7/37bb3bc6170d.jpg[/URL]

So the total answer is

[URL]http://s004.radikal.ru/i208/1108/4f/c35aafd1c20b.jpg[/URL]

Let's calculate it in Math now.

[URL]http://s40.radikal.ru/i090/1108/f8/cf9f67043005.jpg[/URL]

I wonder where Math gets "-" in Exp[] ?

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# Simple integral in Mathematica

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