Result Duplicated! Re: Can Integrate[expr,{x,a,b}] give

*To*: mathgroup at smc.vnet.net*Subject*: [mg81849] Result Duplicated! Re: [mg81827] Can Integrate[expr,{x,a,b}] give*From*: "W. Craig Carter" <ccarter at mit.edu>*Date*: Fri, 5 Oct 2007 04:43:31 -0400 (EDT)*References*: <200710040827.EAA22349@smc.vnet.net> <Pine.OSX.4.64.0710041039510.9889@pruffle.mit.edu>

I take it back. I've just duplicated the result again. I think this IS a bug: InputForm[CylinderIntegrandd\[Theta]d\[Zeta]] is (R*(R - \[Rho]*Cos[\[Alpha] - \[Theta]]))/(3*(R^2 + (z - \[Zeta])^2 + \[Rho]^2 - 2*R*\[Rho]*Cos[\[Alpha] - \[Theta]])^3) InputForm[assumptions] is {R > 0, L > 0, \[Rho] > 0, Element[\[Zeta], Reals], Element[z, Reals], \[Alpha] >= 0, \[Alpha] <= 2*Pi} Integrate[CylinderIntegrandd\[Theta]d\[Zeta], {\[Theta], 0, 2 \[Pi]}, Assumptions -> assumptions] returns 0. I think that this is not correct. Craig PS: I know that the L>0 is superfluous in the assumptions, but I use assumptions over again. On Thu, 4 Oct 2007, W. Craig Carter wrote: > Date: Thu, 4 Oct 2007 10:42:55 -0400 (EDT) > From: W. Craig Carter <ccarter at mit.edu> > To: mathgroup at smc.vnet.net > Subject: (Never Mind? Can't duplicate result!) Re: [mg81827] Can > Integrate[expr,{x,a,b}] give an incorrect result? > > > Dear Mathgroup, > I've tried again to duplicate the results below with a fresh kernal, and I > can't. I am now getting a sensible result. > > Apologies to anyone who might have put time into this. > > Craig > > > > On Thu, 4 Oct 2007, W. Craig Carter wrote: > >> Date: Thu, 4 Oct 2007 04:27:21 -0400 (EDT) >> From: W. Craig Carter <ccarter at MIT.EDU> >> To: mathgroup at smc.vnet.net >> Subject: [mg81827] Can Integrate[expr,{x,a,b}] give an incorrect result? >> >> >> I believe I am getting an incorrect result from a definite >> integration: >> >> InputForm[integrand] is >> (R*(R - rho*Cos[alpha - t]))/(3*(R^2 + rho^2 + (z - zeta)^2 - >> 2*R*rho*Cos[alpha - t])^3) >> >> InputForm[assumptions] is >> {R > 0, L > 0, rho > 0, Element[zeta, Reals], Element[z, Reals], alpha > >> 0} >> >> Integrate[integrand,{t,0,2Pi},Assumptions->assumptions] >> returns 0 >> >> But compare this to: >> (visually integrate...) >> Plot[integrand/.{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z -> >> 1.2},{t,0,2 Pi},PlotRange->All] >> >> (numerically integrate...) >> Plot[NIntegrate[integrand/.{{R -> 1, rho -> 1.1, zeta -> 0, alpha -> 0, z >> -> 1.2},{t,0,tau}],{tau,0,2Pi}, PlotRange->All] >> >> >> Something isn't adding up?? >> >> Thanks, WCC >> >> > >

**References**:**Can Integrate[expr,{x,a,b}] give an incorrect result?***From:*"W. Craig Carter" <ccarter@mit.edu>