Introduction to Integral Calculus

Integral calculus is the important part of calculus as important differential calculus. In the differential calculus we study the relationship between two quantities lets say between Distance and Time, this relationship we usually use in sense of Rate of Change between two variables.

But in Integral Calculus we take the inverse process of the relationship between two quantities, is known as Integration or Anti-Differentiation or Anti- Derivative. The most important application of integral calculus is to compute the area or volume. In ancient time the informal concepts was developed by 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 3th century as regards to find area of circle. In 17th Century John Kepler further developed some important concepts regarding to astronomical investigations to find area of sector and area of an ellipse.

Further the concept of integral calculus was formally developed by Isaac Newton and Gottfried Leibniz; they developed basic concepts to find area and volume. In integral calculus we encounter the different concepts such as area of various geometric shapes, area under the curve by using definite integral, indefinite integral and various practical applications. We also encounter the most important theorem of calculus called “Fundamental Theorem of Calculus” this theorem elaborate the concept that differentiation and integration are opposite operations.