Grade 12 · Mathematics
Antiderivatives
Why it matters
Reversing differentiation.
Advanced20m readingPrerequisite: None
What is an antiderivative?
Short answer
An antiderivative of a function f is a function F whose derivative is f, that is F′(x) = f(x). Finding antiderivatives — also called indefinite integration — reverses differentiation. Because the derivative of a constant is zero, every function has infinitely many antiderivatives differing by a constant C, written ∫ f(x) dx = F(x) + C.
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Frequently asked questions
- Why do antiderivatives include "+ C"?
- Because the derivative of any constant is zero, so adding any constant to an antiderivative gives another valid one.
- How is an antiderivative related to a definite integral?
- The Fundamental Theorem of Calculus evaluates a definite integral using an antiderivative: ∫ₐᵇ f = F(b) − F(a).