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单词 Indefinite integration
释义

Indefinite integration

中文百科

不定积分 Antiderivative

(重定向自Indefinite integration)

在微积分中,一个函数 \begin{smallmatrix} f \end{smallmatrix}
不定积分,也称为原函数反导数,是一个导数等于 \begin{smallmatrix} f \end{smallmatrix}
的函数 \begin{smallmatrix} F \end{smallmatrix}
,即 \begin{smallmatrix} F' = f \end{smallmatrix}
。不定积分和定积分间的关系由微积分基本定理确定。

\begin{matrix} \int f(x)dx = F(x)+C\end{matrix}

其中 \begin{smallmatrix} F \end{smallmatrix}
\begin{smallmatrix} f \end{smallmatrix}
的不定积分。这样,许多函数的定积分的计算就可以简便地通过求不定积分来进行。

英语百科

Antiderivative 不定积分

(重定向自Indefinite integration)
The slope field of F(x) = (x3/3)-(x2/2)-x+c, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant C.
Figure 1.
Figure 2.

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration) and its opposite operation is called differentiation, which is the process of finding a derivative.

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更新时间:2025/6/19 21:44:49