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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This fact which has the similar effect as for the first integral, namely the fundamental theorem of calculus for this second integral also does not hold.
5) It is easy to construct some almost periodic functions f : R [right arrow] X for which there exists M(f) and the fundamental theorem of calculus holds.
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 Fundamental Theorem of Calculus is not easily grasped by students: From experience, it is very hard for students taking up calculus for the first time to understand the equation

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