Re: Integration by substitution
- To: mathgroup at smc.vnet.net
- Subject: [mg29843] Re: Integration by substitution
- From: Ignacio Rodriguez <ignacio at sgirmn.pluri.ucm.es>
- Date: Fri, 13 Jul 2001 04:19:23 -0400 (EDT)
- Organization: UCM
- References: <200107110025.UAA20901@smc.vnet.net> <9iji2g$rik$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Dear Mr Rockmann,
It is true that "sp" and "tp" are single variables, but under the substitution
sp->s/a and tp->t/a, the 2 expressions
Integrate[Sech[s/a]^2 Sech[(t - s)/a]^2, {s, -Infinity, Infinity}]
and
Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}]
are mathematically equivalent. This can be checked by substituting and taking
into account that ds = a dsp and that the integration limits do not change.
J Rockmann wrote:
> ----- Original Message -----
> From: "G. A. Garrett" <ggarrett7 at netscape.net>
To: mathgroup at smc.vnet.net
> Subject: [mg29843] Integration by substitution
>
> > I was wondering if someone could explain to me why the first input
> > below gives no answer while the second input does. It never crossed my
> > mind the Mathematica wouldn't have seen the simple substitution of
> > sp=s/a that produced an answer. I am running ver. 4.0 in a Windows
> > environment. I am basically looking for a characteristic that I can be
> > on the look out for in the future.
> >
> > Integrate[Sech[s/a]^2 Sech[(t - s)/a]^2, {s, -Infinity, Infinity}]
> >
> > Integrate[a Sech[sp]^2 Sech[(tp - sp)]^2, {sp, -Infinity, Infinity}]
> >
> > Gregory
> > --Posted email rarely checked--
> >
> If I'm not mistaken, Mathematica will consider "sp" as a single variable as
> it would "x". Therefore, the two statements are not equivalent to
> Mathematica after any algebraic manipulation has been performed on your
> naming of the variable "sp=sa".
> I hope this helps,
> Jonathan Rockmann
> mtheory at msn.com
--
Ignacio Rodriguez Ramirez de Arellano
Unidad de RMN
Universidad Complutense
Paseo Juan XXIII, 1
Madrid 28040, Spain
Tel. 34-91-394-3288
Fax 34-91-394-3245
e-mail: ignacio at sgirmn.pluri.ucm.es
- References:
- Integration by substitution
- From: ggarrett7@netscape.net (G. A. Garrett)
- Integration by substitution