double integrals seem to give different answers



Richard Hennessy wrote:
> This is a bug, 
...
If you think that  (w^2)^(3/2)   should simplify to  abs(w^3), then you 
inevitably run into problems.
That is what trigsimp, or some component of it, believes.
If you believe, as I do, that there are 2 values, +w^3 and -w^3, and the 
computation should proceed
using Both values until
(a) it is determined that It Doesn't Matter Which You Use.
or
(b) the user (or some other computation) decides that Only One Value 
Works and uses it.
or
(c) you have to produce an answer Including Both Values.

 From this perspective it isn't a bug in integration or trigsimp. And I 
suspect the same trick will catch you in
Mathematica or Maple, if they do the same "simplification". There are a 
large number of system-independent
mathematical "gotchas".

RJF