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What is the integral of 1 x? - Mathematics Stack Exchange 16 Answers to the question of the integral of 1 x 1 x are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers If we allow more generality, we find an interesting paradox For instance, suppose the limits on the integral are from −A A to +A + A where A A is a real, positive number
What is an integral? - Mathematics Stack Exchange A different type of integral, if you want to call it an integral, is a "path integral" These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to find the area under a curve I think of them as finding a weighted, total displacement along a curve
What is the difference between an indefinite integral and an . . . Wolfram Mathworld says that an indefinite integral is "also called an antiderivative" This MIT page says, "The more common name for the antiderivative is the indefinite integral " One is free to define terms as you like, but it looks like at least some (and possibly most) credible sources define them to be exactly the same thing
What is an Integral Domain? - Mathematics Stack Exchange 5 An integral domain is a ring with no zero divisors, i e xy = 0 ⇒ x = 0 or y = 0 x y = 0 ⇒ x = 0 o r y = 0 Additionally it is a widespread convention to disallow as a domain the trivial one-element ring (or, equivalently, the ring with 1 = 0 1 = 0) It is the nonexistence of zero-divisors that is the important hypothesis in the definition