Quick questions on Integration and its applications - TCE Mathematics Methods (Tasmania)

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What are applications to rates?

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Because integration reverses differentiation, integrating a rate of change recovers the total change. If

\dfrac{dV}{dt}

is the rate at which a tank fills, then

\displaystyle\int_{t_1}^{t_2}\frac{dV}{dt}\,dt

is the volume added between

t_1

and

t_2

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