On 5/23/07, Andrej Vodopivec <andrej.vodopivec at gmail.com> wrote:
> There is a difference when maxima can compute the antiderivative. What
> would you expect from integrate(x*tan(x/3), x, 0.0, 1.0). Maxima knows
> how to compute the antiderivative and then returns something
> containing limits. That's why I want a function which computes
> integrals strictly by numerical methods without trying integrate
> first. integrate with numerical bounds should do something different.
I don't see the point of this. If the user wants to be sure a specific
numerical method is used, they'll have to call quad_qags or
whatever directly. There's no guarantee (and there should not be
one) that nintegrate is going to call this or that Quadpack function;
any number of numerical methods might be employed, and one
of them can be, "Compute the antiderivative, if you can, and plug
in the endpoints."
nintegrate would be more useful if its general specification is
"crunch this into a number by any means". We don't have much
to gain by ruling out some useful techniques.
FWIW
Robert