In this section, we will explore the formulas for the different antiderivative rules discussed above in detail. We will discuss the rules for the antidifferentiation of algebraic functions with power, and …

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 …

In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral[Note 1] of a function f is a differentiable function F whose derivative is equal to the …

Find the general antiderivative of a given function. Explain the terms and notation used for an indefinite integral. State the power rule for integrals. Use antidifferentiation to solve simple …

Master antiderivative rules to reverse the process of differentiation and solve problems involving original functions in AP® Calculus.

In these lessons, you will learn the definition of antiderivative, the formula for the antiderivatives of powers of x and the formulas for the antiderivatives of trigonometric functions.

Nov 30, 2025 · Now we can put the ideas of areas and antiderivatives together to get a way of evaluating definite integrals that is exact and often easy. To evaluate a definite integral ∫ a b f …

ANTIDERIVATIVES: RULES, FORMULAS, ETC. Definition: An antiderivative of a function f(x) is a . unction F (x) for which F 0(x) = f(x). Note: The Mean Value Theorem states that all …

Antiderivatives represent the reverse process of derivatives, allowing us to find a function from its derivative. For example, the antiderivative of \ (2x\) is \ (x^2 + c\), where \ (c\) is an unknown …

We used a familiar derivative formula in Example 1c to find the antiderivative of sin x. Our goal in this section is to write the other derivative results for trigonometric functions as indefinite …