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If oil leaks from a tank at a rate of $ r(t) $ gallons per minute at time $ t $, what does $ \displaystyle \int^{120}_0 r(t) \, dt $ represent?

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00:34

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

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.

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If oil leaks from a tank a…

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$\begin{array}{l}{\text { …

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Explain.

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'120 r(t) dt represen…

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Water is leaking from &…

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Oil leaks out of a tanker …

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An oil storage tank ruptur…

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okay if the FT is the volume of the tank than our tea is the derivative of Viotti Soviet prime of tea. So what this means is that the integral from 01 20 r t G t is equivalent to this integral from 0 to 1 20 off the prime of tea. Because remember their equivalent. I just rode out the equivalent statement right over there. But fundamental dilemma calculus part to this is vey of 1 20 minus V of zero. In other words, bound the first found months, the second round. So what this means is that this represents the change in volume of the tank from th zero toe Tia's 1 20 which is the amount of oil leaked in the 1st 2 hours because they're 60 minutes in an hour.

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