Overview

Fundamental Theorem of Calculus


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A sound approach to integration defines the integral as the limit, in a certain sense, of a sum. That this can be evaluated, when f is continuous, by finding an antiderivative of f, is the result embodied in the so-called Fundamental Theorem of Calculus. It establishes that integration is the reverse process to differentiation:

Theorem

If f is continuous on [a, b] and ϕ is a function such that ϕ′(x)=f(x) for all x in [a, b], then

Subjects: Mathematics.


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