**Gottfried Wilhelm Leibniz**

Calculus will be helpful in calculating and counting for mathematics. This calculus has two major branches. They are differential calculus and integral calculus. Differential calculus is nothing but concerning instantaneous rates of change and slopes of curves whereas integral calculus is concerning accumulation of quantities and the areas under and between curves.

Modern calculus we are using these days is expected to be developed by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century. Calculus are often used these days in many fields like science, engineering, and economics.

In modern mathematics, calculus is used as a part of education. In a subject called mathematical analysis, calculus is used as a gateway for advanced and many modern integral forms. In olden days, calculus is generally referred aa 'the calculus of infinitesimals'; 'infinitesimal calculus'. Calculus is often used to name some specific methods like propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.**History of Calculus:**

*Ancient*:

In ancient times, many of the great ideas led to the integral calculus. But later it stopped because they did not followed any systematical approach. In the Egyptian Moscow Papyrus, calculations of area and volume are calculated without using any hard formulas. Those lack of many major components. From the age of Greek mathematics, method of exhaustion was used by Eudoxus, which uses the concept of limit for calculating areas and volumes. This idea was used by Archimedes, who later developed this idea and invented heuristics. This heuristics resemble the methods of integral calculus. Liu Hui from 3rd century AD, later invented this method of exhaustion to find area of circle. Cavalier's principle is later introduced by Zu Zenghzi to find the volume of a sphere.*Medieval*:

Alhazen from middle east is the one who developed a formula for the sum of fourth powers. For calculating the volume of paraboloid, he used the integration of that function by using the sums of integral squares and fourth powers.

*Modern*:

Isaac Newton is known as the father of modern calculus as he introduced many theories. Some of them are product rule and chain rule. He also introduced notions of higher derivatives, Taylor series, and analytical functions. He also developed series of expansions for functions, along with frictional and irrational powers. Let us see what John von Neumann said about calculus.The calculus can be considered as the first achievement of modern mathematics. It is difficult to overestimate the importance of calculus. I think it defines more unequivocally better than any other methods of mathematics. The inception of modern mathematics, the system of mathematical analysis, which is a logical development of these can be constitute the great development of advance technologies.

*Integral Calculus*:

It is the study of definitions, properties, applications of two different concepts, the definite integral, and the indefinite integral. The process of finding an integral value is called Integration.