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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?

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

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Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Boston College

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Video Transcript

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.

Topics

Integrals

Integration

Kayleah T.

Harvey Mudd College

Samuel H.

University of Nottingham

Boston College

Lectures

Join Bootcamp