>>>>> "Alasdair" == Alasdair McAndrew <amca01 at gmail.com> writes:
Alasdair> If I enter, say:
Alasdair> define(t(x),taylor(f(x),x,a,10));
Alasdair> where f(x) is a symbolic (that is, undefined) function,
Alasdair> I get an expression full of derivatives, as I
Alasdair> should. ?How can I integrate this series term by term?
Alasdair> ?Does Maxima have any flags or functions which will
Alasdair> allow me to integrate a symbolic derivative?
As an example,
(%i10) taylor(f(x),x,a,1);
(%o10) f(a)+('at('diff(f(x),x,1),x = a))*(x-a)
(%i11) integrate(%,x,a,a+h);
(%o11) (h^2*('at('diff(f(x),x,1),x = a))+2*f(a)*h)/2
In 2D, which is easier to read:
!
2 d !
h (-- (f(x))! ) + 2 f(a) h
dx !
!x = a
(%o13) -------------------------------
2
Isn't that the correct answer? What exactly were you expecting?
Ray