Difference between integration and differentiations
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- Integration
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other.
- Uses of Integration
Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start with finding the area under the curve of a function like this: What is the Area Under Y = F(X)?
- Example of Integration
In Electrical Engineering, Calculus (Integration) is used to determine the exact length of power cable needed to connect two substations, which are miles away from each other.
- Differentiation
In simple way you can understand that differentiation is the derivative is the instantaneous rate of change of a function with respect to one of its variables, or, differentiation is a process of finding the derivative, or rate of change, of a function.
- Uses of Differentiation
Differentiation allows us to find rates of change.
it allows us to find the rate of change of velocity with respect to time (which is acceleration).
It also allows us to find the rate of change of x with respect to y, which on a graph of y against x is the gradient of the curve.
Example of Differentiation
x²+y²=1. Implicit differentiation helps us find dy/dx even for relationships like that.
This is done using the chain rule, and viewing y as an implicit function of x.
For example, according to the chain rule, the derivative of y² would be 2y⋅(dy/dx).