Gosse Michel <michel.gosse@ac-poitiers.fr> writes:
> (C2) integrate(sqrt(2-2*cos(t)),t,0,2*%pi);
>
> Is SIN(t)^2+COS(t)^2+2*COS(t)+1 positive, negative, or zero?
>
> positive;
> (D2) 0
>
> This is however impossible, because the function is positive...
> Maple returns 8 !
Thanks for reporting this. Maxima tries to solve this problem via
indefinite integration and then substitutes the endpoints of the
interval. There is a bug in both parts.
1) integrate(sqrt(1-cos(x)),x) returns a result which is valid on
[0,%pi] but not on (%pi, 2*%pi], where it would take the opposite
sign.
2) This means that integrate(sqrt(1-cos(x)),x,0,%pi) should work, but
it returns 0, too, although for a completely different reason, viz.
the second COND clause of SIN-COS-INTSUBS1 in src/defint.lisp.
I think that both SIN-COS-INTSUBS and SIN-COS-INTSUBS1 are wrong
and that it would be better to pass the arguments in question
directly to INTSUBS. But then again, there should be some problem
which these functions try to address (there's even a comment).
Wolfgang