V2EX constant of integration

Constant of Integration

Definition / 释义

积分常数:在求不定积分时出现的一个任意常数(常写作 C),用来表示同一导数对应的一族原函数;因为常数的导数为 0,所以不定积分结果必须加上它。(在不同初始条件下,C 的取值不同。)

Pronunciation / 发音(IPA)

/knstnt v ntren/
/knstnt v ntren/

Examples / 例句

\(\int 2x\,dx = x^2 + C\), where \(C\) is the constant of integration.
\(\int 2x\,dx = x^2 + C\),其中 \(C\) 是积分常数。

When you use an initial condition like \(y(0)=3\), you can determine the constant of integration and get a unique solution.
当你使用像 \(y(0)=3\) 这样的初始条件时,就能确定积分常数,从而得到唯一解。

Etymology / 词源

constant 来自拉丁语 constare(“站稳、保持不变”),表示“不变的量”;integration 来自拉丁语 integrare(“使完整”),在数学中指“积分(把变化累积成整体)”。合起来 constant of integration 就是“积分过程中必须补上的不变常量”。

Related Words / 相关词

Literary Works / 文献与著作中的用例

  • Calculus James Stewart
  • Thomas’ Calculus George B. Thomas, Maurice D. Weir, Joel Hass
  • Calculus and Analytic Geometry George B. Thomas & Ross L. Finney
  • A Course of Pure Mathematics G. H. Hardy
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