Student Support Forum: 'Integrate problem in version 4' topicStudent Support Forum > General > "Integrate problem in version 4"

 < Previous Comment Help | Reply To Comment | Reply To Topic
 Author Comment/Response Forum Moderator email me 09/27/00 06:06am >The following integral works in version 3 but not in version 4. The result I have given is from version 3.>Why does it fail in version 4? > >In[1]:= >Integrate[4*Pi*r^2*(Sin[\[Kappa]*r]*r*Erf[r*\[Xi]])/(\[Kappa]*r), > {r, 0, Infinity}, Assumptions -> > {Im[\[Kappa]] == 0, Im[\[Xi]] == 0, Re[\[Xi]] > 0, Re[\[Kappa]] > 0, > \[Kappa] > 0, \[Xi] > 0}] > >Out[1]:= >-((Pi*(\[Kappa]^4 + 2*\[Kappa]^2*\[Xi]^2 + 8*\[Xi]^4))/ > (E^(\[Kappa]^2/(4*\[Xi]^2))*\[Kappa]^4*\[Xi]^4)) > > >Version 4 gives the error: > >Integrate::''idiv'' : ''Integral of \!\(r\^2\\ \(\(Erf[\(\(r\\ \[Xi]\)\)]\)\)\\ \ >\(\(Sin[\(\(r\\ \[Kappa]\)\)]\)\)\) does not converge on \!\({0, \ >\*InterpretationBox[\''\[Infinity]\'', DirectedInfinity[1]]}\).'' > > >My version evaluates to: > >In[6]:= >\$Version > >Out[6]= >''4.0 for Microsoft Windows (July 16, 1999)'' > >In[5]:= >\$ReleaseNumber > >Out[5]= >1 > >Thank you very much. > >Kevin ======= Since this integral is not convergent as an ordinary integral, the Version 4 result shows the intended behavior. The Version 3 result could be considered correct if Integrate is understood as a generalized integration operation, but that is not the intended design. The intended default behavior is for Integrate to check for basic convergence as in Version 4. A convenient way to see that the integral is not convergent as an ordinary integral is to look at a plot of the integrand for numerical values of the symbolic parameters. For example, after replacing both of the symbolic parameters by 1, the input Plot[4 Pi r^2 (Sin[r] r Erf[r])/(r), {r, 0, 100}] reveals an integrand with ever-increasing oscillations which can not be expected to converge. You can get the Version 3 result in Version 4 by including the GenerateConditions -> False option so that Integrate does not check for convergence of the integral: Integrate[4 Pi r^2 (Sin[\[Kappa] r] r Erf[r \[Xi]])/(\[Kappa] r), {r, 0, Infinity}, GenerateConditions -> False] This is the intended way of getting the Version 3 result in Version 4. Forum Moderator Response by David Withoff URL: ,

 Subject (listing for 'Integrate problem in version 4') Author Date Posted Integrate problem in version 4 Kevin Hase 09/27/00 05:59am Re: Integrate problem in version 4 Forum Modera... 09/27/00 06:06am
 < Previous Comment Help | Reply To Comment | Reply To Topic