7.80 bug in integrating abs(...) (26.3.96)

7.80.1 A. van der Meer

In release 4 signum() still causes trouble:

> Int(Int(abs(y-x^2),x=-1..1),y=0..2); 
 
                         2    1 
                        /    / 
                       |    |          2 
                       |    |   | y - x  | dx dy 
                       |    | 
                      /    / 
                      0    -1 
 
> value(%); 
 
                                  2 
 
 
> Int(Int(abs(y-x^2),y=0..2),x=-1..1); 
 
                         1    2 
                        /    / 
                       |    |          2 
                       |    |   | y - x  | dy dx 
                       |    | 
                      /    / 
                      -1   0 
 
> value(%); 
 
                                  46 
                                  -- 
                                  15
 

The last answer is correct. R3 gives no answer for the first integral. The best policy is to avoid abs() or signum() and always use piecewise().

The same result up to Maple 6.

With Maple 7 and Maple 8 you get with value(%); evalf(%); 3.216988933 instead of 3.066666835, what you get with evalf(Int(Int( ... )); (U. Klein)