fundamental theorem of calculus

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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 functional is differentiable on [a,b ] and F(x) = ƒ(x) for every x in [a,b ], and if G is any function on [a,b ] such that G ′(x) = ƒ(x) for all x in [a,b ], then
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Curvature and the shape of space and the generalization of the fundamental theorem of calculus are also gone into at length.
As expected, a high point of first-year calculus is the discussion of the Fundamental Theorem of Calculus (FTC).
He discusses the ancients, east of Greece, curves, indivisibles, quadrature, the fundamental theorem of calculus, notation, chords, zero over zero, and rigor.
Second, the weakly sequential continuity of G is a direct consequence of the fundamental theorem of calculus for Lebesgue integration (see e.
In 1672, before he formulated the fundamental theorem of calculus, he published on properties of sequences of sums and differences of sums.
Unfortunately, the fundamental theorem of calculus stated in [3, Theorem 2, pp.
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].
While they don't offer a proof of the Fundamental Theorem of Calculus, they do a decent job of making clear, in English, what it means.
The advantage of the Definition 7 above is that the fundamental theorem of calculus is being imbedded in the definition.
By the fundamental theorem of calculus, for all y [member of] [0, T] we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and consequently
The first three applets illustrate the important idea behind the Fundamental Theorem of Calculus.