Re: Question on PrincipalValue in Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg80696] Re: Question on PrincipalValue in Integrate
- From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
- Date: Wed, 29 Aug 2007 04:16:23 -0400 (EDT)
- References: <fb0u04$j8r$1@smc.vnet.net>
"Jung-Tsung Shen" <jushen at gmail.com> wrote: > A question on the "PrincipalValue" in the option of the command, > Integrate: > > Mathematica (v5.0 Mac) gives the following command > > Integrate[1/(y-x), {x, -d, d}, PrincipalValue -> True] > > the answer > > If[y > 0 && y < d, I Pi - Log[d - y] + Log[d + y], Integrate[1/(-x + y), > {x, -d, d}, Assumptions -> d ? y || y ? 0]] > > But shouldn't the first part of the answer by - Log[d - y] + Log[d + y], > without the I Pi? Using version 5.2: In[5]:= Assuming[0 < y < d, Integrate[1/(y-x), {x, -d, d}, PrincipalValue -> True]] Out[5]= - Log[d - y] + Log[d + y] as desired. David