Date: Jan 11, 2013 10:22 PM
Author: Alex Krasnov
Subject: Re: wrong result when computing a definite integral

Integrate takes the integration variables in prefix order, so perhaps you 
meant the following:

In: Integrate[Exp[I*Sqrt[3]*y], {y, -Pi, Pi}, {x, -2*Pi, 2*Pi}]
Out: (8*Pi*Sin[Sqrt[3]*Pi])/Sqrt[3]

Alex


On Thu, 10 Jan 2013, Dexter Filmore wrote:

> hi group,
>
> i run into this problem today when giving a bunch of easy integrals to mathematica.
> here's a wolfram alpha link to the problem:
> http://www.wolframalpha.com/input/?i=Integrate%5BExp%5BI+Sqrt%5B3%5Dy%5D%2C%7Bx%2C-2Pi%2C2Pi%7D%2C%7By%2C-Pi%2CPi%7D%5D#
>
> the integrand does not depend on the 'x' variable, the inner integration should only result in a factor of 4Pi, and the correct result is a real number, yet the below integral gives a complex number which is far off from the correct value:
> Integrate[Exp[I Sqrt[3] y], {x, -2 Pi, 2 Pi}, {y, -Pi, Pi}] -> -((4 I (-1 + E^(2 I Sqrt[3] Pi)) Pi)/Sqrt[3])
>
> from some trial and error it seems the result is also incorrect for non-integer factors in the exponential.
>