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If $ x $ is measured in meters and $ f(x) $ is me…

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Problem 56 Easy Difficulty

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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Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Related Topics

Integrals

Integration

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Top Calculus 1 / AB Educators
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Integrals - Intro

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.

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40:35

Area Under Curves - Overview

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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Video Transcript

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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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
Grace He

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University of Michigan - Ann Arbor

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Lectures

Video Thumbnail

05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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