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In Section 4.7 we defined the marginal revenue function $ R'(x) $ as the derivative of the revenue function $ R(x) $, where $ x $ is the number of units sold. What does $ \displaystyle \int^{5000}_{1000} R'(x) \, dx $ represent?

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$$R(5000)-R(1000)$$

00:22

Frank Lin

00:27

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

Baylor University

Boston College

Lectures

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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.

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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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$\begin{array}{l}{\text { …

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In Section 4.7 we defined …

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In Section 4.6 we defined …

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In Section 4.5 we defined …

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In Section 3.7 we defined …

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Suppose that the marginal …

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The figure shows graphs of…

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Let $R(x)$ be the revenue…

uh Since we will learn the fundamental theorem of calculus, We learned that the interval from a 1000 to 5000 of our prime of X is equal to, It's now just are of the upper bound of 5000 Minour are of the lower bound of 1000. Um So that's from the fundamental theorem of calculus that the anti derivative cancels out that derivative. And so what we're looking at is the difference and uh a revenue between selling 1000 and 5000 units, I think it was just a number of units. I don't have to worry about thousands of units. Um So that's really what it represents. Um And it's based off the fundamental theorem of calculus there.

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