AP Calculus AB and BC glossary

Antiderivative

An antiderivative of a function is any function whose derivative equals it. Because the derivative of a constant is zero, a function has infinitely many antiderivatives, all differing from one another by a constant.

F(x)=f(x)    F is an antiderivative of fF'(x) = f(x) \iff F \text{ is an antiderivative of } f

The family of all antiderivatives is the indefinite integral, which is why the constant of integration appears there. On a connected interval, knowing one antiderivative determines all of them.

Every antiderivative you find can be checked by differentiating it, which takes seconds and catches most sign and coefficient errors before they propagate.

Appears in: Unit 6: Integration and Accumulation