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If $ x $ is measured in meters and $ f(x) $ is measured in newtons, what are the units for $ \displaystyle \int^{100}_0 f(x) \, dx $?
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00:56
Frank Lin
00:25
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Campbell 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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um The quick answer as we work, let's say, a function is measured in units and you find the derivative, you usually have to divide by whatever the, you know, the units are for X. And it's usually in time, whatever the X units are. Um So when I'm trying to get at is as we go backwards, instead of just saying would cancel out, I would say you multiply by the X units and that would cancel out whatever these are. So the reason I bring that to your attention is because when you give the directions and I really don't care what these numbers are. I go ahead and write a mouth though. F of X Dx and you know, the units for F. R. News and you're doing this, then you need to multiply uh by the X in this case is meters. So these are newton meters are your units when you work out that way. Apparently those are called jewels.
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