The antiderivative rules in calculus are basic rules that are used to find the antiderivatives of different combinations of functions. As the name suggests, antidifferentiation is the reverse process of …

While derivatives break down motion and change into their smallest parts, antiderivatives do the opposite, they build up the original function from its changes.

Nov 10, 2020 · For now, let’s look at the terminology and notation for antiderivatives, and determine the antiderivatives for several types of functions. We examine various techniques for finding …

The graphs of antiderivatives of a given function are vertical translations of each other, with each graph's vertical location depending upon the value C. More generally, the power function has antiderivative if …

Dec 1, 2025 · Antiderivatives include a family of functions that differ by a constant C, because the derivative of a constant is zero. Thus, the general form of the antiderivative is: F (x) = ∫f (x) dx = F (x) …

Jun 6, 2025 · However, it is helpful to connect antiderivatives to differentiation through antiderivative rules. According to the relationship known as FUN-6.C.1, the derivative of an antiderivative returns …

Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a function plus …

While derivatives provide the rate of change of a function, antiderivatives help us recover the original function from its derivative. This concept is crucial as we progress in calculus.

The antiderivative of a sum of several terms is the sum of their antiderivatives. This follows from the fact that the derivative of a sum is the sum of the derivatives of the terms. And similarly, multiplying a …

The need for antiderivatives arises in many situations, and we look at various examples throughout the remainder of the text. Here we examine one specific example that involves rectilinear motion.