Antiderivative - Wikipedia
WEBIn calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f.
Antiderivative Calculator - Symbolab
WEBFree antiderivative calculator - solve integrals with all the steps. Type in any integral to get the solution, steps and graph.
4.9: Antiderivatives - Mathematics LibreTexts
WEBNov 10, 2020 · For a function \(f\) and an antiderivative \(F\), the functions \(F(x)+C\), where \(C\) is any real number, is often referred to as the family of antiderivatives of \(f\). For example, since \(x^2\) is an antiderivative of \(2x\) and any antiderivative of \(2x\) is of the form \(x^2+C,\) we write \[\int 2xdx=x^2+C.\]
4.10 Antiderivatives - Calculus Volume 1 - OpenStax
WEBHighlights. Learning Objectives. 4.10.1 Find the general antiderivative of a given function. 4.10.2 Explain the terms and notation used for an indefinite integral. 4.10.3 State the power rule for integrals. 4.10.4 Use antidifferentiation to solve simple initial-value problems.
4.1: Introduction to Antiderivatives - Mathematics LibreTexts
WEBNov 24, 2021 · Definition 4.1.1. A function \ (F (x)\) that satisfies. \begin {align*} \dfrac {d} {dx} F (x) &= f (x) \end {align*} is called an antiderivative of \ (f (x)\text {.}\) Notice the use of the indefinite article there — an antiderivative.
12.1 The Anti-derivative - MIT Mathematics
WEBThe antiderivative is the name we sometimes, (rarely) give to the operation that goes backward from the derivative of a function to the function itself.
3.4: Antiderivatives of Formulas - Mathematics LibreTexts
WEBMay 28, 2023 · To evaluate a definite integral b ∫ af(t)dt, we can find any antiderivative F(t) of f(t) and evaluate F(b) − F(a). The problem of finding the exact value of a definite integral reduces to finding some (any) antiderivative F of the integrand and then evaluating F(b) − …
Antiderivatives – Calculus Tutorials - Harvey Mudd College
WEBAntiderivatives. Let f(x) be continuous on [a, b]. If G(x) is continuous on [a, b] and G ′ (x) = f(x) for all x ∈ (a, b), then G is called an antiderivative of f. We can construct antiderivatives by integrating.
5.1: Antiderivatives and Indefinite Integration
WEBNov 25, 2023 · An antiderivative of \(f(x)\) is a function \(F(x)\) such that \(F'(x) = f(x)\). The set of all antiderivatives of \(f(x)\) is the indefinite integral of \(f\) , denoted by \[\int f(x) \ dx.\]
Chapter 12: The Anti-Derivative - MIT Mathematics
WEBThe anti-derivative is an operation that undoes differentiation, Since the derivative of a constant is 0, the anti-derivative gives an answer that says nothing about constant terms. The rules for differentiation each give rise to information on calculating anti-derivatives.
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