antiderivative of a real function

原函数

Analysis, Measure & PDE · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

An antiderivative of f on an open real interval I is a differentiable function F on I with F'(x)=f(x) at every point of I.

实函数 f 在开区间上的原函数，是在该区间可导并且导数处处等于 f 的函数 F。

Example

F(x)=x3/3+7F(x)=x^3/3+7 is an antiderivative of x2x^2.

Usage and distinctions

On an interval, two antiderivatives differ by one constant; on a disconnected domain the constants may differ between components.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. OpenStax — Calculus Volume 1§4.10, The Reverse of Differentiation, Definition and Theorem 4.14 · Checked 2026-10-14

Translation sources

  1. 北京大学数学科学学院 — 数学分析（实验班）课程介绍第一部分 一元微积分学，六、不定积分：原函数 · Checked 2026-10-14
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