antiderivative
antiderivative — 名詞
1. A function F whose derivative equals the original function f — in other words, a
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).
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
The captain asked the team to find the antiderivative of each velocity function.
隊長要求團隊找出每個速度函數的反導數。
Amir computed the antiderivative of f(x)=cos x and wrote sin x + C in his homework notebook.
Amir 算出 f(x)=cos x 的反導數，並在作業本上寫下 sin x + C。
wrote sin x + C
Haruto used the antiderivative to solve the differential equation for population growth.
Haruto 利用反導數來解人口成長的微分方程。
- find the antiderivative
- compute the antiderivative
- antiderivative of [function]
- family of antiderivatives
- general antiderivative
- indefinite integral
the most common alternative name in calculus textbooks; used interchangeably with antiderivative
- primitive function
less common outside advanced mathematics; mostly used in European textbooks
- antiderivative function
a slightly longer form that emphasises that the term is a function
- 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
同根字
- derivative名詞C1
- derivative形容詞C1
- differentiate動詞C1
- differentiation名詞C1
- integral名詞C1
- integral形容詞C1
- integration名詞C1