It's based on Maple's intat() function, which is what it's dsolve() returns in these cases. See http://www.maplesoft.com/support/help/Maple/view.aspx?path=intat&term=intat.
I think I preferred this over Integral(f(x), (x, a, y)) because if the user eventually substitutes f(x) for something that can be integrated, then there will be an f(a) laying around, which will technically be correct because it will be added to an arbitrary constant, but it will not be absorbed or anything, because constantsimp() is only called within dsolve(). Of course, in analysis, definite integrals are studied, because of how the integral is defined. For example, the Reimann integral is defined using partitions of an interval, and from that you can prove things like the fundamental theorem of calculus and things like two different functions with the same derivative will have integrals that differ only by a constant. So it only makes sense to define the definite integral, and then to derive the definite integral from it using the theorems. But in practice, particularly for solving ODE's, actually using definite integrals is important. Aaron Meurer On Mar 28, 2010, at 11:06 PM, Ondrej Certik wrote: > On Sun, Mar 28, 2010 at 9:59 PM, Aaron S. Meurer <asmeu...@gmail.com> wrote: >> The None is essentially inert substitution, so maybe it should work like >> Integral(f(x), x)(y). I'd like to get the same syntax working for >> f(x).diff(x)(y) to mean f'(y) (the derivative of f evaluated at y) as per >> issue 1620. >> >> By the way, I implemented this to allow general case solutions from >> dsolve(), for example (from the docstring of ode.ode_separable): > > I see. I think a better way is to implement the proper substitution in > derivatives (resp. evaluation of the derivative at a point), and the > same for integrals, but I think you can just use > > integrate(f(y), (y, a, x)) > > to represent a primitive function, where "a" is a constant. > > Btw, maybe someone can correct me, but in my experience, it seems that > definite integrals is all that is needed, all the primitive functions > are just use in calculus classes, but otherwise it's imho better to > use definite integrals. > > Ondrej > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sy...@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sy...@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
