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If the units for $ x $ are feet and the units for $ a(x) $ are pounds per foot, what are the units for $ da/dx $? What units does $ \displaystyle \int^8_2 a(x) \, dx $ have?
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Calculus 1 / AB
Indefinite Integrals and the Net Change Theorem
Oregon State University
University of Michigan - Ann Arbor
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.
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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Okay, X is in feet and a sub X is in pounds per foot. So what kind of units are D A D X. Okay. So the adx means take the derivative with respect to X. Of a. So I a is in pounds per feet and you're taking its derivative with respect to feet. So then it will be in pounds per feet per feet. So it was already in pounds per foot. And then you took as derivative with respect to feet. Okay, So that will be in pounds per foot per foot per foot foot or pounds per square foot or foot square? All right then. What about the integral? Okay, so remember the integral is an area, so X. Is in feet? So feet here and why? Which is a Cybex is in pounds per feet? Pounds per foot. So let's just draw a rectangle here. If we're finding this area you would be multiplying X times Y. So it would be in pounds per foot Times feet, so it would be in pounds. Yeah, sure. The integral is in pounds. You take away the foot. Okay. But the derivative is in pounds per square foot. So you've added a foot in there? Yeah, I have
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