Math
Antiderivatives.
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
Real-world.
- 1 The antiderivative of 2x is x² + C, since d/dx(x² + C) = 2x
- 2 The antiderivative of cos(x) is sin(x) + C
Key Fact
∫ xⁿ dx = xⁿ⁺¹/(n+1) + C for n ≠ −1