
Re: wrong result when computing a definite integral
Posted:
Jan 12, 2013 9:51 PM


Unless there's some issue of branches of complex functions involved that I'm missing, it should not matter here which order of integration you use  since the limits of integration are constants. However, if you wrap each integrand in ComplexExpand,
a = Integrate[ComplexExpand[Exp[I*Sqrt[3]*y]], {x, 2*Pi, 2*Pi}, {y, Pi, Pi}] b = Integrate[ComplexExpand[Exp[I*Sqrt[3]*y]], {y, Pi, Pi}, {x, 2*Pi, 2*Pi}]
then you obtain the same result:
{a, b} // InputForm {(8*Pi*Sin[Sqrt[3]*Pi])/Sqrt[3], (8*Pi*Sin[Sqrt[3]*Pi])/Sqrt[3]} a == b True
On Jan 11, 2013, at 10:22 PM, Alex Krasnov <akrasnov@eecs.berkeley.edu> wrote:
> 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] > > Thu, 10 Jan 2013, Dexter Filmore wrote: > >> 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%2C2Pi%2C2Pi%7D%2C%7By%2CPi%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 noninteger factors in the exponential.
 Murray Eisenberg murray@math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 5491020 (H) University of Massachusetts 413 5 (W) 710 North Pleasant Street fax 413 5451801 Amherst, MA 010039305

