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wrong result when computing a definite integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg129392] wrong result when computing a definite integral
*From*: Dexter Filmore <liquid.phynix at gmail.com>
*Date*: Thu, 10 Jan 2013 21:39:16 -0500 (EST)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
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.
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