Integration
Mathematically, “The process of finding a function, whose differential coefficient is known (given), is called integration.”
Hence, integration is the inverse process of differentiation. Integration and differentiation are two operations which are inverse to each other.
Let 
. Then, by definition, integration of 
with respect to x is 
. We shall use the notation
………….[1]
- The symbol
is called the symbol of integration. 
is called the notation of integration of with respect to x.- x is called the variable of integration (independent variable).
Physical Meaning of Integration
Physically, since 
Or 
Taking summation of all the differentials, we have 
Or 
…………………….[2]
When dx approaches to zero, the summation is replaced by integration and we write 
………………..[3]
It means, physically, the method of integration is used to sum up the effect of a continuous varying function.
It is important to note that the sign 
is used for summation of discrete values, while sign is used for summation of continuous function.
How to use integration in physics?
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Indefinite Integration
Since, differentiation of a constant factor is zero i.e. 
We get, 
So, by Eq [1], we get 
……………..[4]
Where, C is constant independent of x. The value of constant C can be determined using some limiting conditions.
Definite Integration
When a function is integrated between definite limits, the integral is called definite integral. Usually, these limits are the initial and final value of the independent variable x. In this case no constant is used and we write eq [4] as
………………. [5]
Thus, physically 
gives the change in the value of for x = a to x = b.