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Bug? Analytical integration of cosines gets the sign wrong

• To: mathgroup at smc.vnet.net
• Subject: [mg107168] Bug? Analytical integration of cosines gets the sign wrong
• From: K <kgspga at googlemail.com>
• Date: Thu, 4 Feb 2010 06:32:55 -0500 (EST)

Hello everyone,

the analytical integration in Mathematica 7.01.0 on Linux x86 (64bit)

faultyInt =
 Integrate[Cos[ph]*1/Pi*Cos[4*ph]*Cos[2*ph], {ph, Pi, 3/2*Pi}]

gives as result:

19/(105 \[Pi])

which is as a decimal number

N[faultyInt]

0.0575989

The numerical integration

NIntegrate[Cos[ph]*1/Pi*Cos[4*ph]*Cos[2*ph],{ph,Pi,3/2*Pi}]

gives

-0.0575989

which I believe is correct by judging from the plot

Plot[Cos[ph]*1/Pi*Cos[4*ph]*Cos[2*ph], {ph, Pi, 3/2*Pi},
 PlotRange -> {-1/Pi, 1/Pi}]

and because the quadgk function in another system gives the same
negative result.  Could anyone try this at home (or work, rather)
and confirm or disprove it?
Thanks,
K.

• Follow-Ups:
  • Re: Bug? Analytical integration of cosines gets the sign wrong
    • From: Louis Talman <talmanl@gmail.com>
  • Re: Bug? Analytical integration of cosines gets the sign
    • From: Mark McClure <mcmcclur@unca.edu>