# [Maxima] integration asks to many questions

Detlef Schmicker d.schmicker at physik.de
Fri Apr 13 12:45:56 CDT 2007

```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
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)
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*(x1-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)

```