F(x) is a function before I attempt to integrate such a function over a certain interval, what I do is check if the interval is a subset of the function's domain, if not then its not integrable.
And it doesn't matter if the function includes any types of discontinuities on the interval or includes any indifferentiable points.
And for indefinite integrals(basically anti-derivatives) they always exist as long as the function exists.
Additional question: is it possible that the interval a certain function is being integrated on isn't a subset in the domain of the 'new' function (the anti-derivative) thus isn't integrable?
Wednesday, 21 January 2015
calculus - Validity Check: Every function is integrable on its domain, regardless to continuity and differentiablitty.
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