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单词 antiderivative
释义

antiderivative

Given a real function f, any function ϕ such that ϕ′(x) = f(x), for all x (in the domain of f), is an antiderivative of f. If ϕ1 and ϕ2 are both antiderivatives of a continuous function f, defined on an interval, then ϕ1(x) and ϕ2(x) differ by a constant. In that case, the notation

may be used for an antiderivative of f, with the understanding that an arbitrary constant can be added to any antiderivative. Thus,

where c is an arbitrary constant, is an expression that gives all the antiderivatives of f.

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更新时间:2025/4/29 19:55:41