Mathematically the basic concept of addition, summation and other calculations has great importance. The calculation process requires much of the time to learn and then practice. Integration and differentiation are in one of them.
The integration and differentiation are known to be the inverse processes, as integration is the name of addition of small components into the one simple unit whereas the differentiation is the change of one variable with respect to the other variable.
In this article you will be able to learn about the integration, differentiation, the relationship between the integration and differentiation. Their importance in daily routine and their uses. So the detailed description of integration, differentiation and their relationship can be explained as follows.
What is integration?
The word integration is derived from the Latin word which means “whole”. It is defined as the act of integrating, adding or uniting the small and discrete data into a whole form. It is also known as the process of calculating definite and indefinite integrals.
Definite integrals can be calculated by using antiderivatives. The application of integration is used to find different things just like central points, volume, area (specifically area under the curve).
The primary reason for using integration is to enhance the capabilities of functions. Integration’s use in real life has a great importance in different fields and these fields usually include the physics, engineering, model demonstrations and graphical representations.
What is differentiation?
In simple words the differentiation is referred to the act of differentiating. The process of differentiation includes the modification of one value into the many. Like the change of rate of one component with respect to the rate of change of another component and from simple one to complex one.
Mathematically the differentiation is the process of finding the change in function, derivative of function, that is based on one of its variables.
Differentiation is used in solving the many life problems either related to industries financial resources and organizations policies. The basic amount of change in maximization or minimization can also be evaluated in terms of different functions through differentiation.
Relationship between integration and differentiation
Both integration and differentiation are the concepts of calculus, mathematics. It belongs to continuous change. The basic purpose of finding the relationship between the integration and differentiation can be elaborated in different ways. Some of the points can be as follows.
- The integration is used for addition of small and discrete data whereas the differentiation is used in the study of small changes of one quantity with respect to the change of another quantity.
- The integration is related to adding up the simple components whereas the differentiation focuses on the rate of change.
- The integration is simply used in finding the area under the curve of a function whereas the differentiation is used in finding the slope of a function at a point.
- The integration is considered the definite integrals of functions over an interval whereas the differentiation are derivatives that are considered at a point.
- The relationship of integration is known to be the reverse process of differentiation.
- The relationship of integration and differentiation is as when calculating the differential equation, it is necessary to calculate the one or more integrals.
- Both integration and differentiation helps in daily life. Such as increasing the capabilities of organizations and their productions.
Related: You may also read Useful Info Regarding Expected Value and Significant Figures on Newstowns educational blogs.
Conclusion
The integration and differentiation relationship is known to be the inverse or reverse process. The integration mainly calculates the areas under the curve and derivatoves helps in finding the rate of change of variables with one another. Both of these functions are used in a continuous change which is very crucial to daily life.
The integration and differentiation are helpful in finding and calculating the functionality of organizations, firms, industries and other businesses. Students could also get benefitted by learning the integration and differentiation by using the best integral calculator and you can also find the derivative calculator. This article will help you understand the reverse relationship of integration with differentiation. Their use in daily life problems that most of the organizations face increasing their functionalities.
