Virgil wrote: > In article <earle.jones-86B16E.firstname.lastname@example.org>, > Earle Jones <email@example.com> wrote: > >> In article <firstname.lastname@example.org>, >> G Patel <email@example.com> wrote: >> >>> What is the antiderivative of 1/(2*sqrt(x)) ? >>> >>> Is it, sqrt(x) in its entirety, or sqrt(x), x>0 ? > But sqrt(x) in its entirety has only one more point of definition, > namely x = 0, than its restriction to x > 0, so why worry? I would say you are slightly taking the wrong perspective. All that is required is that an antiderivative be differentiable on the domain of the first function, whatever that domain is. The first function is not defined at x=0 so, unless you have some supplementary conditions, you can extend it to x=0 or even the negative numbers, however you wish.