RE: (Newbie) More confusion with integral of absolute vals
- To: mathgroup at smc.vnet.net
- Subject: [mg9385] RE: [mg9367] (Newbie) More confusion with integral of absolute vals
- From: jmthomas <jmthomas at cybercable.tm.fr>
- Date: Sun, 2 Nov 1997 01:02:18 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Your question has been rather disappointing me and I'm not sure my
answer can help you in any way:
I tried Integrate[Abs[x],{x,a,b}] and, as you did, had to abort the
evaluation after some ten minutes.
I must admit that, if Mathematica cannot answer properly, it should at
least answer quickly. I tried to submit your integral to "The
integrator" on Wolfram Research site, the answer was: Mathematica was
not able to do the integral you requested. If you think = the integral
can in fact be done, please send mail to = webmaster at integrals.com so
it can be analyzed by our mathematical = development group.
Beside the fact "the integrator" performs indefinite integrals only, I
leave you submit your case to them.
Anyway, this could help:
As far as Abs is a general function for real AND complex numbers, it
certainly dizzles the kernel. So I wrote:
absoluteValue[x_]:=3DIf[x>=3D0,x,-x] which defines Abs[x] for real
only. And then f[a_,b_]:=3DIntegrate[absoluteValue[x],{x,a,b}] Please
notice the fact that this definition is a delayed definition. Then,
giving values to a and b returns a correct numerical result, which
might be what you are looking for.
Hope this helps.
----------------------------------------------- Jean-Marie THOMAS
Conseil et Audit en Ing=E9nierie de Calcul jmthomas at cybercable.tm.fr
www.cybercable.tm.fr/~jmthomas
-----Message d'origine-----
De: L. Dwynn Lafleur [SMTP:lafleur at usl.edu] Date: samedi 1 novembre 1997
09:34
=C0: mathgroup at smc.vnet.net
Objet: [mg9367] (Newbie) More confusion with integral of absolute vals
Suppose I want to integrate the absolute value of x over the range a->b.
It's simple enough in Maple V Release 4:
> ii:=3Dint(abs(x),x=3Da..b);
2 2
ii :=3D 1/2 b signum(b) - 1/2 a signum(a)
> assume(0<a,a<b);
> ii;
2 2
1/2 b~ - 1/2 a~
where the tildes (~) indicate there are assumed properties for a and b.
If I try the same thing in Mathematica 3.01, I get
In[1]:=3D ii=3DIntegrate[Abs[x],{x,a,b}] Out[1]=3D $Aborted
In other words, Mathematica cannot perform the integral and I must abort
the evaluation. Even if I try to place Assumptions in the Integrate
function, the integration is not performed. What am I missing here?
Can't the integration be performed as easily in Mathematica as it is in
Maple?
--
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D L. Dwynn Lafleur
Professor of Physics
The University of Southwestern Louisiana Lafayette, Louisiana (USA)
lafleur at usl.edu
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D