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Re: Bug? Analytical integration of cosines gets the sign wrong

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107346] Re: Bug? Analytical integration of cosines gets the sign wrong
  • From: WetBlanket <wyvern864 at gmail.com>
  • Date: Wed, 10 Feb 2010 03:35:02 -0500 (EST)
  • References: <hkeb9k$b5$1@smc.vnet.net>

On Feb 4, 5:33 am, K <kgs... at googlemail.com> wrote:
> 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.
If One substitutes the sequence, {1.9, 1.99, 1.999, ... 2.0}
Mathematica gets the correct answer for as long as I tried except, of
course for 2.0.


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