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Shown is the graph of traffic on an Internet service provider's T1 data line from midnight to 8:00 AM. $ D $ is the data throughput, measured in megabits per second. Use the Midpoint Rule to estimate the total amount of data transmitted during that time period.

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00:04

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Harvey Mudd College

Idaho State University

Boston College

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.

02:32

Shown is the graph of traf…

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02:08

03:56

10:37

03:06

The accompanying graph sho…

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02:16

08:11

okay. We know the central from zero to a of D of t did Cheap is gonna be 1/3 time's d of T zero plus four times D of t one plus two times D of T, too. It was four times D v D three plus two terms D of de Flore plus four times D of G five plus two times DVD six plus four times D of G seven close five times Sorry, plus one times d of t eight. Using a calculator for this you end up with 4.36 however, are not done. We have to multiply this by 3600 seconds because that's the number of seconds in an hour, seconds and seconds. Cancel. This is dimensional analysis and we end up with 15 696 mega bits.

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