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Explain exactly what is meant by the statement that "differentiation and integration are inverse processes."
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00:04
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 3
The Fundamental Theorem of Calculus
Integration
Missouri State University
University of Michigan - Ann Arbor
University of Nottingham
Lectures
05:53
In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.
40:35
In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.
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Okay. We know that if F is integrated and then the result of this is differentiated, we arrived back the original function. Remember the fundamental theme of calculus. And then you must understand the fact that if we consider the two parts of the fundamental form of cockles part one in part to these imply that differentiation and integration are inverse prop processes, each one does what the other does. Therefore, they are in verse.
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