Keyword Analysis & Research: derivative of an indefinite integral

cuemath.com

https://www.cuemath.com/calculus/derivative-of-an-integral/

WEBThe derivative of an indefinite integral of a function is the function itself. i.e., d/dx ∫ f (x) dx = f (x) The derivative of a definite integral with constant limits is 0. i.e., d/dx ∫ a b f (t) dt = 0. Up to $30 cash back

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khanacademy.org

https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-7/v/antiderivatives-and-indefinite-integrals

WEBThose would be derivatives, definite integrals, and antiderivatives (now also called indefinite integrals). When you learn about the fundamental theorem of calculus, you will learn that …

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libretexts.org

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.01%3A_Antiderivatives_and_Indefinite_Integration

WEBDefinition\(\PageIndex{1}\): Antiderivatives and Indefinite Integrals. Let a function \(f(x)\) be given. An antiderivative of \(f(x)\) is a function \(F(x)\) such that \(F'(x) = f(x)\). The set of …

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lamar.edu

https://tutorial.math.lamar.edu/Classes/CalcI/IndefiniteIntegrals.aspx

WEBIf \(F\left( x \right)\) is any anti-derivative of \(f\left( x \right)\) then the most general anti-derivative of \(f\left( x \right)\) is called an indefinite integral and denoted, \[\int{{f\left( x …

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symbolab.com

https://www.symbolab.com/study-guides/openstax-calculus1/antiderivatives.html

WEBFor each of the following functions, find all antiderivatives. [latex]f\left (x\right)=3 {x}^ {2} [/latex] [latex]f\left (x\right)=\frac {1} {x} [/latex] [latex]f\left (x\right)=\text …

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libretexts.org

https://math.libretexts.org/Bookshelves/Calculus/Elementary_Calculus_2e_(Corral)/05%3A_The_Integral/5.01%3A_The_Indefinite_Integral

WEBThe following indefinite integrals are just re-statements of the corresponding derivative formulas for the six basic trigonometric functions: Since \(\ddx(e^x) = e^x\), then: …

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khanacademy.org

https://www.khanacademy.org/math/old-integral-calculus/indefinite-integrals

WEBAbout this unit. If f is the derivative of F, then F is an antiderivative of f. We also call F the "indefinite integral" of f. In other words, indefinite integrals and antiderivatives are, …

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libretexts.org

https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/05%3A_Integration/5.03%3A_The_Fundamental_Theorem_of_Calculus

WEBDividing by b − a gives us. m ≤ 1 b − a∫b af(x)dx ≤ M. Since 1 b − a∫b af(x)dx is a number between m and M, and since f(x) is continuous and assumes the values m and M over [a, b], …

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lamar.edu

https://tutorial.math.lamar.edu/classes/calci/IntegralsIntro.aspx/IndefiniteIntegrals.aspx

WEBAs with derivatives this chapter will be devoted almost exclusively to finding and computing integrals. Applications will be given in the following chapter. There are really two types of …

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