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Re: wrong result when computing a definite integral

• To: mathgroup at smc.vnet.net
• Subject: [mg129413] Re: wrong result when computing a definite integral
• From: danl at wolfram.com
• Date: Fri, 11 Jan 2013 22:25:24 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
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• References: <kcntuu$f8f$1@smc.vnet.net>

On Thursday, January 10, 2013 8:38:22 PM UTC-6, 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.

Thank you for the example. I reported this as a bug. I apologize for any inconvenience it may have caused.

Daniel Lichtblau
Wolfram Research