antiderivative

/ˌan-tē-di-ˈri-və-tiv ˌan-ˌtī-/ (ame, mw)

antiderivative — 名詞

1. A function F whose derivative equals the original function f — in other words, a

1.名詞C1
釋義

反導數

微分後可得原函數的函數

A function F whose derivative equals the original function f — in other words, a function obtained by reversing the process of differentiation. Every antiderivative of a given function differs by a constant (usually written as C).

例句

Kofi found the antiderivative of f(x)=2x and wrote x² plus C as his answer.

Kofi 找出 f(x)=2x 的反導數，並寫下答案 x²＋C。

found the antiderivative of

Rin checked her calculus homework by differentiating the antiderivative she had found.

Rin 把求出的反導數再微分一次，以此檢查她的微積分作業。

differentiating the antiderivative

同義詞
反義詞
  • derivative

    the function obtained by differentiating the original function — the inverse operation

文法句型

the antiderivative of [function]

用法筆記

In calculus, the symbol ∫ f(x) dx is used to denote the general antiderivative of f, also called the indefinite integral. The constant C is always added to represent the family of all possible antiderivatives.

常見錯誤

❌The antiderivative of 2x is x².
✅The antiderivative of 2x is x² + C.
💡Every antiderivative must include a constant term because differentiating any constant gives zero.
❌Antiderivative and derivative are the same process.
✅Antiderivative reverses differentiation, while derivative measures the rate of change.
💡They are inverse operations.