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Suppose that a volcano is erupting and readings of the rate $ r(t) $ at which solid materials are spewed into the atmosphere are given in the table. The time $ t $ is measured in seconds and the units for $ r(t) $ are tonnes (metric tons) per second.

(a) Give upper and lower estimates for the total quantity $ Q(6) $ of erupted materials alter six seconds.(b) Use the Midpoint Rule to estimate $ Q(6) $.

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Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

Harvey Mudd College

Baylor University

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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