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Problem 68 Medium Difficulty

Water flows into and out of a storage tank. A graph of the rate of change $ r(t) $ of the volume of water in the tank, in liters per day, is shown. If the amount of water in the tank at time $ t = 0 $ is $ 25,000 L $, use the Midpoint Rule to estimate the amount of water in the tank four days later.

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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

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Integrals

Integration

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Calculus: Early Transcendentals

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Top Calculus 1 / AB Educators
Grace He

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Catherine Ross

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Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Calculus 1 / AB Courses

Lectures

Video Thumbnail

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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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