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