# Understanding the Calculus Concepts of Differentiation and Integration

## Chapter 35 - More Principles of Industrial Instrumentation (Animated)

The following animation shows the calculus concepts of differentiation and integration (with respect to time) applied to the filling and draining of a water tank.

[animation_calculus_tankfilling]

The animation shows two graphs relating to the water storage tank: one showing the volume of stored water in the tank ($$V$$) and the other showing volumetric flow rate in and out of the tank ($$Q$$). We know from calculus that volumetric flow rate is the time-derivative of volume:

$Q = {dV \over dt}$

We also know that change in volume is the time-integral of volumetric flow rate:

$\Delta V = \int_{t_0}^{t_1} Q \> dt$

Thus, the example of a water storage tank filling and draining serves to neatly illustrate both concepts in relation to each other.

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