7.74 bug in int Maple V.51 to Maple 8 (24.9.01)

7.74.1 Guy Gendron

It sounds like int is having problem with integrating the following functions.

> z_modele_1:=x*cos(x)^3; 
> z_modele_2:=sin(x)+x*cos(x)-sin(x/2); 
> evalf(int(abs(z_modele_2-z_modele_1),x=0..5)); 
> evalf(Int(abs(z_modele_2-z_modele_1),x=0..5)); 
 
                                             3 
                       z_modele_1 := x cos(x) 
 
             z_modele_2 := sin(x) + x cos(x) - sin(1/2 x) 
 
                             2.041317817 
 
                             5.959032441
 

The correct answer is 5.95... .

These differences have been noticed both in Maple 6 (build=16401) and Maple 7 (build=96223) on Wintel.

7.74.2 Adri van der Meer (30.10.01)

This is a bug in int indeed.

Maple 6:

> K := int(abs(z_modele_2-z_modele_1),x=0..X): 
> eval(K, X=0 ); 
 
                                -11/9
 

If you (only) need a numerical approximation of an integral, it is always better to use the inert form Int.

Because:

evalf(Int...) makes a numerical approximation of the integral;

evalf(int...) first integrates symbolically and calculates a numerical approximation of the result.