Introduction to Integral Calculus

Integral calculus is an important part of calculus, as important as differential calculus. In differential calculus we study the relationship between two quantities, let's say between distance and time. For this relationship we usually use the rate of change between two variables.

In integral calculus, however, we take the inverse process of the relationship between two quantities. This is known as integration, anti-differentiation or anti-derivative. The most important application of integral calculus is to compute the area or volume of a shape. In ancient times, the informal concepts were developed by the Greek mathematicians Archimedes (287 BC – 212 BC) and Eudoxus (410 BC – 347 BC). They developed the approximate area of different geometric shapes, and these basic methods were also developed by Chinese mathematician Liu Hui around the 3rd century to find the area of a circle. In the 17th Century John Kepler further developed some important concepts regarding astronomical investigations to find the area of a sector and the area of an ellipse. The concept of integral calculus was formally developed further by Isaac Newton and Gottfried Leibniz; they developed basic concepts to find area and volume.

In integral calculus we encounter different concepts such as the area of various geometric shapes, the area under the curve by using the definite integral, the indefinite integral and various practical applications. We also encounter the most important theorem of calculus called the “Fundamental Theorem of Calculus.” This theorem elaborates upon the concept that differentiation and integration are opposite operations.