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

• To: mathgroup at smc.vnet.net
• Subject: [mg107178] Re: [mg107168] Bug? Analytical integration of cosines gets the sign wrong
• From: "David Park" <djmpark at comcast.net>
• Date: Fri, 5 Feb 2010 03:19:26 -0500 (EST)
• References: <30308427.1265284507356.JavaMail.root@n11>

```It looks like a bug. Also if we evaluate using the indefinite Integrate and
LimitsBracket we obtain the minus sign.

Needs["Presentations`Master`"]

LimitsBracket[
Integrate[(Cos[ph] Cos[4 ph] Cos[2 ph])/\[Pi], ph], {ph, \[Pi],
3 \[Pi]/2}]
% // EvaluateLimitsBracket

[(2 Sin[ph]+2/3 Sin[3 ph]+2/5 Sin[5 ph]+2/7 Sin[7 ph])/(8 \[Pi])](3 \[Pi])/2
\[Pi]  (* which displays as a conventional textbook limits bracket
expression *)

-(19/(105 \[Pi]))

David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

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.

```

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