fundamental theorem of calculus

Basic principle of calculus. It relates the derivative to the integral and provides the principal method for evaluating definite integrals (see differential calculus; integral calculus). In brief, it states that any function that is continuous (see continuity) over an interval has an antiderivative (a function whose rate of change, or derivative, equals the function) on that interval. Further, the definite integral of such a function over an interval a < x < b is the difference F(b) − F(a), where F is an antiderivative of the function. This particularly elegant theorem shows the inverse function relationship of the derivative and the integral and serves as the backbone of the physical sciences. It was articulated independently by Isaac Newton and Gottfried Wilhelm Leibniz.

fundamental theorem of calculus [¦fən·də¦ment·əl ¦thir·əm əv ′kal·kyə·ləs]

(mathematics)

Given a continuous function ƒ(x) on the closed interval [a,b] the functionalis differentiable on [a,b] andF′(x)= ƒ(x) for everyxin [a,b], and ifGis any function on [a,b] such thatG′(x) = ƒ(x) for allxin [a,b], then

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No references found			Both of them are built on the strong foundation of analytical geometry linked by the fundamental theorem of calculus. Calculus Help How to Get Started by Robert Duval / Reference and Education community Unfortunately, the fundamental theorem of calculus stated in [3, Theorem 2, pp. Almost periodic functions with values in p-frechet spaces, 0 < p < 1 by Gal, Sorin G.; N'Guerekata, Gaston M. / Global Journal of Pure and Applied Mathematics The Fundamental Theorem of Calculus (FTC) states that if F(t) has a continuous derivative in an open interval I, then for a and b in I, [[integral]. Computers and mathematical philosophies in educational trends by Khadivi, M.R. / Journal of Computers in Mathematics and Science Teaching			fundamental frequency fundamental frequency of the voice fundamental group fundamental interaction Fundamental interactions fundamental interval fundamental jelly Fundamental Length Fundamental Library of the Social Sciences fundamental mode fundamental motion fundamental number Fundamental Orders fundamental particle fundamental quantity fundamental region fundamental sequence fundamental series fundamental star places Fundamental State Laws of the Russian Empire fundamental strength fundamental substance fundamental tensor fundamental theorem of algebra fundamental theorem of arithmetic fundamental theorem of calculus Fundamental Tone fundamental unit fundamental wavelength Fundamentalism fundamentalism, Christian fundamentalism, Islamic fundholding fundic gland Fundic Glands fundula fundus Fundy Fundy National Park Fundy, Bay Fundy, Bay of Funen Funeral funeral customs Funeral Feast Funeral Urn Funev, Ivan Fünfkirchen Fungal biotechnology fungal diseases Fungal Diseases of Plants			Fundamental regime Fundamental regime Fundamental region Fundamental research Fundamental research Fundamental research Fundamental research Fundamental research Fundamental Research on Economic Agents Fundamental Review of Infrastructure Fundamental Review of Military Budget Fundamental rights Fundamental rights Fundamental rights Fundamental Rights Agency Fundamental Rodent Experiments Supporting Health fundamental rule Fundamental sequence fundamental series fundamental star places Fundamental State Laws of the Russian Empire fundamental strength fundamental substance Fundamental system fundamental tensor Fundamental theorem of algebra Fundamental theorem of algebra Fundamental theorem of arithmetic Fundamental theorem of arithmetic Fundamental Theorem of Asset Pricing fundamental theorem of calculus Fundamental theorem of finite abelian groups Fundamental theorem of finite abelian groups Fundamental Theorem of Integral Calculus Fundamental Theorem of Moment Invariants Fundamental theorem of natural selection Fundamental theorem of number theory Fundamental theorem of poker Fundamental theorem of projective geometry Fundamental theorem of projective geometry Fundamental Theorem of Software Engineering Fundamental theorem of symmetric functions Fundamental theorem of the calculus Fundamental Theorem of Welfare Economics Fundamental theorems of calculus Fundamental theory Fundamental tone Fundamental tone fundamental tones Fundamental Train Frequency Fundamental unit Fundamental unit Fundamental unit Fundamental units Fundamental units Fundamental units Fundamental values Fundamental values Fundamental values Fundamental values Fundamental values