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If $ w'(t) $ is the rate of growth of a child in pounds per year, what does$ \displaystyle \int^{10}_5 w'(t) \,dt $ represent?

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00:35

Frank Lin

00:27

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Oregon State University

Baylor University

University of Nottingham

Boston College

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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all right, we are given the derivative of the function of W. T. To represent the rate of growth of the child in palace per year and were asked then to determine what this represents our first things. First, we know that the integral of a derivative we'll need you to the original function so that this would go away. We also have to take account are five in our 10 here. The way we do it is we take the top number for the integral and subtracted by the bottom number of the integral. So you say, Well, w ci 10 to 5 people to W 10. So what would WB when t is equal to 10, subtracted by W on t z Go too far, right? And that is the representation of this integral here. All right, well, I hope that clarifies the question. Thank you so much for watching

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