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If $ f(x) $ is the slope of a trail at a distance of $ x $ miles from the start of the trail, what does $ \displaystyle \int^5_3 f(x) \, dx $ represent?
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00:25
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Campbell University
Baylor University
University of Michigan - Ann Arbor
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.
00:49
If $f(x)$ is the slope of …
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$\begin{array}{l}{\text { …
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00:53
Suppose that $\int_{3}^{5}…
01:48
Suppose that $\int_{5}^{-3…
00:22
If we know $$\int_{2}^{5} …
01:00
Given $\int_{-.5}^{3} f(x)…
01:19
Find $ \displaystyle \int^…
00:59
$$\text { Given } \int_{0}…
00:54
Express as one integral.
01:47
Evaluate the integral usin…
by the total change. The arm we know we have the integral from 3 to 5 of eat prime of acts de acts on We know by the trouble changed the arm. This is equivalent to e of the top bound, which is five majesty of the lower bound, which is three. Okay, this represented the change in elevation between exes three miles. Shoot X is five miles. That's what this interval represents.
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