use assumptions for the integration

Axel Vogt — Mon, 22 Nov 2010 03:00:02 Z

Sometimes Maple seems to be a bit stupid, so help it

Int(Int((r^2+r*cos(theta))*r*(a^2-r^2)^(1/2),r = 0 .. a),theta = 0 .. 2*Pi);
value(%) assuming (0 < a, a < 2*Pi);
         2 Pi    a
        /       /
       |       |     2                     2    2 1/2
       |       |   (r  + r cos(theta)) r (a  - r )    dr dtheta
       |       |
      /       /
        0       0


                                  5
                               4 a  Pi
                               -------
                                 15

But - is that really stupid? Only in some sense, I think - but I am not sure
(though it always makes me grumbling): if you think complex, then it is not
clear to have an ordering, or if the path is a (real) line providing an order ...

So give merci to the generality and feed assumtions in case.

PS: providing input in ASCII would make it more easy to copy/paste for answering.

Assumption

Robert Israel — Mon, 22 Nov 2010 08:19:51 Z

You don't need the a < 2*Pi, but you do need a > 0. In fact, for a < 0 the result should be -4*a^5*Pi/15.

assuming real

Alejandro Jakubi — Mon, 22 Nov 2010 09:06:25 Z

Just assuming real:

int((r^2+r*cos(theta))*r*(a^2-r^2)^(1/2),[r = 0 .. a,theta = 0 .. 2*Pi]) assuming real;
                               5
                         4/15 a  Pi signum(a)

MaplePrimes - answers and comments on Question, Is there a way to help Maple evaluate this triple integral?

use assumptions for the integration

Assumption

assuming real