Calculus – Meaning, Types & Uses

Mathematics is one of the most worrisome subjects of all. The mathematical questions, the calculations, different concepts, etc are confusing for many. The problem is not just faced by students in school or aspirants of competitive exams but also by adults who are well employed. It is also seen that many individuals change their field of study because they couldn’t handle the hardships caused by mathematics. During the preparation of any competitive exam, if the exam syllabus includes mathematics it makes aspirants anxious and they start seeking help from here and there. Even after hours of problem-solving and studying if they get stuck while solving a question paper on mathematics it becomes very frustrating for them.

In mathematics, one of the most stressed topics is calculus. Not just learners who are weak at mathematics but also who are good at it fail in calculus courses because it has a slightly complex theory, concepts, and calculations associated with it. However, if one follows the rules and properties well, calculus can be really easy to study. It is just like algebra, with daily practice one can get used to the hefty concepts and complex calculations. 

In this article, we will be discussing integral calculus, its meaning, and its various applications as a mathematical tool. Make sure you read the content provided below well to be able to familiarise yourself with integral calculus and come at ease with it. 

What Is Calculus?

From the points mentioned below let us understand calculus. Go through the points mentioned below thoroughly.

• The word calculus is a Latin word that originally means small pebbles. 
• It was formed in the late 17th century by Issac Newton and Gottfried Wilhelm Leibniz. 
• It denotes courses of elementary mathematical study, which are mainly devoted to the study of functions and limits. 
• Calculus is originally called infinitesimal calculus. Just like geometry is the study of shapes, and algebra is the study of arithmetic operation, calculus is the mathematical study of continuous change. 
• It has two branches, integral calculus, and differential calculus.  

What Is Integral Calculus?

The points mentioned below will help you understand integral calculus better than before. Therefore, read all the points carefully.

• As mentioned above integral calculus is a branch of calculus. It is involved in the accumulation of quantities and areas under or between curves.
• In technical language, integral calculus is the study of two related linear operators called the indefinite integral and the definite integral. 
• The indefinite integral is also known as antiderivative and has no upper and lower limit of integration.
• Whereas the definite integral is also known as a Riemann Integral contains the upper and lower limits i.e. start and the end value is known as a definite integral. 

What Are The Applications Of Integral Calculus?

Let us understand the applications of integral calculus from the points mentioned below.

There are several methods of calculations among which are functions, differentiation, and integration. 

• Applications of Integrals are applied in various fields like mathematics, architecture, medical science, engineering. 
• The most common application of integral calculus is the calculation of areas or irregular shapes in a two-dimensional space.
• The major use of integral formulas is seen at the time of finding areas under simple curves or bounded by a curve, a line, or area between two curves beside them; it is also used to find the centre of mass of an area having a curved side.
• The common applications of integrals are also seen in physics while calculating the centre of gravity, mass, the moment of inertia of vehicles, the momentum of satellites, etc.