antiderivative: meaning, definition, pronunciation and examples
C2Formal Technical
Quick answer
What does “antiderivative” mean?
A function whose derivative is the given function.
Audio
Pronunciation
Definition
Meaning and Definition
A function whose derivative is the given function; essentially the 'reverse' of differentiation in calculus.
In a broader mathematical sense, refers to a family of functions that differ by a constant, whose differentiation yields the original function. It is the fundamental concept behind integration.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. The term is standardized internationally in mathematics.
Connotations
Purely technical in both varieties.
Frequency
Equally frequent in academic and advanced educational contexts in both regions.
Grammar
How to Use “antiderivative” in a Sentence
The antiderivative of [FUNCTION]Find the antiderivative for/of [FUNCTION][FUNCTION] has an antiderivativeVocabulary
Collocations
Examples
Examples of “antiderivative” in a Sentence
verb
British English
- N/A (Not a verb)
American English
- N/A (Not a verb)
adverb
British English
- N/A (Not an adverb)
American English
- N/A (Not an adverb)
adjective
British English
- N/A (Rarely used adjectivally. Can be seen in 'antiderivative function'.)
American English
- N/A (Rarely used adjectivally. Can be seen in 'antiderivative function'.)
Usage
Meaning in Context
Business
Never used.
Academic
Exclusively used in mathematics, physics, and engineering education and research, particularly in calculus courses and papers.
Everyday
Never used in everyday conversation.
Technical
Core term in calculus, analysis, and applied mathematics.
Vocabulary
Synonyms of “antiderivative”
Vocabulary
Antonyms of “antiderivative”
Watch out
Common Mistakes When Using “antiderivative”
- Forgetting the '+ C' (constant of integration) when writing the general antiderivative.
- Confusing the antiderivative with the definite integral (which gives a numerical area).
- Using 'derivative' when 'antiderivative' is meant.
FAQ
Frequently Asked Questions
In most introductory contexts, they are used synonymously. Technically, the indefinite integral refers to the family of all antiderivatives (hence the '+ C'), while an antiderivative can refer to one specific function from that family.
Because differentiation of a constant is zero. If F(x) is an antiderivative of f(x), then F(x) + C, where C is any constant, will also have the same derivative, f(x). The '+ C' represents this infinite family of solutions.
Not every function has an antiderivative that can be expressed in terms of elementary functions (like polynomials, exponentials, trigonometric functions). Some functions require special functions or numerical methods for their antiderivatives.
Its main uses are in evaluating definite integrals (via the Fundamental Theorem of Calculus), solving differential equations, and finding quantities from their rates of change (e.g., position from velocity).
A function whose derivative is the given function.
Antiderivative is usually formal technical in register.
Antiderivative: in British English it is pronounced /ˌæn.ti.dɪˈrɪv.ə.tɪv/, and in American English it is pronounced /ˌæn.t̬i.dɪˈrɪv.ə.t̬ɪv/ || /ˌæn.taɪ.dɪˈrɪv.ə.t̬ɪv/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “N/A (Technical term, no idioms)”
Learning
Memory Aids
Mnemonic
Think of ANTIderivative: it's ANTI or 'against' the derivative. It reverses the process of taking a derivative.
Conceptual Metaphor
Reversal/Undoing (The antiderivative 'undoes' what the derivative did, like subtraction undoes addition).
Practice
Quiz
What is the relationship between an antiderivative and a derivative?