antiderivative
/ˌan-tē-di-ˈri-və-tiv ˌan-ˌtī-/ (ame, mw)
antiderivative — noun
1. A function F whose derivative equals the original function f — in other words, a
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.
found the antiderivative of
Rin checked her calculus homework by differentiating the antiderivative she had found.
differentiating the antiderivative
The captain asked the team to find the antiderivative of each velocity function.
Amir computed the antiderivative of f(x)=cos x and wrote sin x + C in his homework notebook.
Haruto used the antiderivative to solve the differential equation for population growth.
- 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.