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The process of differentiation is likened to finding instantaneous rate of change, or tangent to a curve.
For example, when we talk of speed we take change in the distance and change in time and divide the two. But when we are talking about changes in time of the order of milliseconds, and even smaller, and limting it to go to zero. We have the process of differentiation. It then gives the instantaneous value.
The process of integration is opposite to the differentiation. It gives area under the given curve. Also surface and volume generated by revolution of a curve.