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Importance of Integration in Maths

Thursday, March 19, 2020

Integration is an important concept of Mathematics. It is one of the two calculus other than differentiation.

 Integration is a method of adding discrete data, especially in large scale industries. 

While on a small scale, we can easily add the quantities by simple calculations, but for sectors which have discrete data, it is not easy to do the calculations. 

Integrals are used to determine many useful quantities, such as areas, volumes, displacement, etc.

Integration is the process to figure out the cumulative impact of forces that experience variations as they work on a body while it is in motion. Integrals allow us to define the collective effect of kinetic energy.

In a widespread, the concept of limit is used in calculus, where algebra and geometry are implemented. Limits help us in the study of the result of points on a graph such as how they get closer to each other until their distance is almost zero. We would learn here two types of integrals. They are definite integral and indefinite integral.

An integral that includes the upper and lower limits is said to be a definite integral, whereas indefinite integrals are defined without upper and lower limits. But, why do we need to calculate the integrals? What are the applications of integrals? The answer to these questions are:
       To find the area between the curves
       To find the distance, velocity and acceleration
       To find the volume
       To find the work done
       To find the kinetic energy
       To find the probability
       To find the average value of a function 
       To find the surface area

Now how do we calculate these quantities using integrals? So, there are two methods by which integration can be done, i.e., either by substitution or by parts.

In the substitution method, either of the given integral is transformed into a simple form by substituting the independent variable by others. In calculus, the substitution method is also termed as the “Reverse Chain Rule” or “U-Substitution Method”. Integration by parts is a unique technique of combination of two functions when they are multiplied with each other. This method is also called partial integration.

Integration is the usual method to find complete change when you know tiny changes. The term "Integrate" is a Latin word and it means "make whole".

Integration in Other Subjects

In Chemistry, integration is beneficial. Chemical kinetics use the rate of change of concentration of several species. Upon integrating, we get the relationship between mass and time. Integration is also used to determine some formulae of thermodynamics.

Integration is widely used in Physics, as well. Gauss's law for electrostatics, Ampere's law for magnetism, Maxwell's equations, all of them use integration. Many physical queries involving mechanics, electromagnetism, atomic and nuclear phenomena, etc. can be easily answered using integration.
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