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The current in a wire is defined as the derivative of the charge: $ I(t) = Q'(t) $. (See Example 3.7.3.) What does $ \displaystyle \int^b_a I(t) \, dt $ represent?

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The amount of charge (number of electrons) that pass through an intersection of the wire from time a to time b.

00:36

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Oregon State University

Baylor University

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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remember, in this context, I of tea is equivalent to Q prime of teeth, and we know the integral from A to B of I of T D T is equivalent to being to grow from A to B of Q prime of T D T, which is equivalent to queue of B minus. Q of A. That's the fundamental theme of calculus. So what? This means that this represents the change in amount of the charge from time of a two time of B, so the amount of charge number electrons that pastor intersection of the wire from time to time be.

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