Re: Bug? Analytical integration of cosines gets the sign wrong
- To: mathgroup at smc.vnet.net
- Subject: [mg107214] Re: Bug? Analytical integration of cosines gets the sign wrong
- From: Fred <fred at unknown.com>
- Date: Fri, 5 Feb 2010 03:25:57 -0500 (EST)
- References: <hkeb9k$b5$1@smc.vnet.net>
K, I get the same wrong answer with Mathematica 7.0.1.0 under Windows 64-bit In[1]:= f[x_] = Cos[x]*Cos[2*x]*Cos[4*x]/Pi; Integrate[f[x], {x, Pi, 3 Pi/2}] // N NIntegrate[f[x], {x, Pi, 3 Pi/2}] Out[2]= 0.0575989 Out[3]= -0.0575989 Mathematica does get it right if we use indefinite integral In[4]:= fPrim[x_] = Integrate[f[x], x]; fPrim[3 Pi/2] - fPrim[Pi] // N Out[5]= -0.0575989 Mathematica even gets it right if we use the definite integral with bounds not involving Pi? In[6]:= lowerbound = 3.141592654; upperbound = 3 lowerbound/2; Integrate[f[x], {x, lowerbound, upperbound}] // N Out[8]= -0.0575989 IMHO this is a bug, and should be reported to http://support.wolfram.com/submitabug.cgi Regarde Arnold Smit On 4-2-2010 12:33, K 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. >