> declare(g,oddfun);
> integrate( (x-a)^2*g(x-a),x,0,2*a) --> no change. [should be same as
> problem above].
>
> R
seems that we have to help maxima finding that ()^2 is even w.r.t its
argument.
(%i1) kill(all);
(%o0) done
(%i1) declare(g, oddfun);
(%o1) done
(%i2) integrate( (x-a)^2*g(x-a),x,0,2*a);
Is a positive, negative, or zero?p;
(%o2) integrate((x-a)^2*g(x-a),x,0,2*a)
(%i3) changevar(%, y=x-a, y, x);
(%o3) integrate(y^2*g(y),y,-a,a)
(%i4) ev(%, nouns);
(%o4) 0
It is still not clear to me why integrate needs an extra even function
to use the oddness of g in a symmetric integral (the function 1 would do
the job?)
--Martin