> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Detlef Schmicker
> Sent: Friday, April 13, 2007 11:54 PM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] integration asks to many questions
>
> By the way:
>
> if I use a self defined function
> dint(f,v,a,b):=subst(b,v,integrate(f,v))-subst(a,v,integrate(f,v));
>
> instead of integrate for the integral with bounds, no
> questions are ask,
> and the result seems to be OK.
>
> Is there a reason, build in integral is working differently?
Yes. Your program relies on the "Fundamental Theorem of Integral Calculus"
whose conditions may not be fulfilled by the integrand. It may have
singularities between a and b.
Incidentally, your program can be made twice as fast by computing the
integral only once.
Dint(f,v,a,b):= block([FF:integrate(f,v)], subst(b,v,FF)-subst(a,v,FF));
>
> Detlef
>
> Am Freitag, den 13.04.2007, 19:45 +0200 schrieb Detlef Schmicker:
> > Hi,
> >
> > I wonder if somebody is working on integration. The
> integral I needed is
> > somewhat complex, but it is solved e.g. by mathematica without any
> > questions.
> >
> > One problem of cause is, missing two dimensional
> integration, therefore
> > I am not able to answer the question to the sign of cos(kp x2).
> >
> > But other questions are not necessary too. Maybe maxima
> should try all
> > options, and check if the result really differs. In my case
> it does not,
> > independend of a number of answers.
> >
> > I would help fixing, but I would not love to be the only
> one working on
> > the integration. I read in the archive, somebody already
> had the wish to
> > have multidimensional integration. Here is a reason, it is
> necessary.
> > Otherwize I have to split the integral by hand to have
> correct answers
> > to cos(kp x2).
> >
> > Detlef
> >
> > (sorry, the output is not always readable in here, don't
> know a better
> > way)
> >
> > detlef at sarge:~$ maxima
> >
> > Maxima 5.10.0 http://maxima.sourceforge.net
> > Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
> > Distributed under the GNU Public License. See the file COPYING.
> > Dedicated to the memory of William Schelter.
> > This is a development version of Maxima. The function bug_report()
> > provides bug reporting information.
> > (%i1) p:(1+
> >
> a*cos(kp*x1)+a*cos(kp*x2)+a*a*cos(kp*x1)*cos(kp*x2))*sin(kp*(x
> 1-x2)/4);
> > kp (x1 - x2) 2
> > (%o1) sin(------------) (a cos(kp x1) cos(kp x2) + a cos(kp x2) + a
> > cos(kp x1)
> > 4
> >
> > + 1)
> > (%i2) p2:p*(1+c*cos(kp*(x1+x2)/2));
> > kp (x1 - x2) 2
> > (%o2) sin(------------) (a cos(kp x1) cos(kp x2) + a cos(kp x2) + a
> > cos(kp x1)
> > 4
> >
> kp (x2 +
> > x1)
> > + 1) (c
> > cos(------------) + 1)
> > 2
> > (%i3)
> integrate(integrate(p2^2,x1,-4*%pi/kp,4*%pi/kp),x2,5*%pi/kp/2,7*%
> > pi/kp/2);
> >
> > Is kp positive or negative?
> >
> > p;
> > Is a zero or nonzero?
> >
> > n;
> > Is a c positive, negative, or zero?
> >
> > n;
> > Is c zero or nonzero?
> >
> > n;
> > Is a positive or negative?
> >
> > n;
> > Is c positive or negative?
> >
> > p;
> > Is cos(kp x2) positive, negative, or zero?
> >
> > p;
> > Is kp positive or negative?
> >
> > p;
> > 2 4 3 2 2 2 2
> > (%o3) ((3 %pi a - 40 %pi a + 24 %pi a - 72 %pi a + 12 %pi ) c
> > 4 2 3 2 2
> 2
> > 4
> > + (16 %pi a - 24 %pi a + 152 %pi a - 48 %pi a + 48
> %pi) c + 6 %pi
> > a
> > 3 2 2 2 2
> > - 48 %pi a + 24 %pi a - 96 %pi a + 24 %pi )/(6 kp )
> > (%i4)
> >
> >
> > _______________________________________________
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> > Maxima at math.utexas.edu
> > http://www.math.utexas.edu/mailman/listinfo/maxima
> >
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