Antiderivatives

Math

Definition

A function F(x) is an antiderivative of f(x) if F′(x) = f(x). Finding antiderivatives reverses differentiation. The general antiderivative includes a constant C because the derivative of any constant is zero.

Examples

  • The antiderivative of 2x is x² + C, since d/dx(x² + C) = 2x
  • The antiderivative of cos(x) is sin(x) + C
Key Fact

∫ xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1

Related Terms

Fundamental theorem Chain rule Accumulation functions Area between curves

Study This Concept

Practice antiderivatives with free review games in these units:

AP Calculus AB Unit 6: Integration and Accumulation