Calculus! many students get fear with this branch of mathematics as it is consider as one of the difficult branch of Math. The word Calculus is derived from Latin word, which means calculating something and used for counting anything. Calculus covers a wide area of modern mathematics it mainly focuses on limits, functions, derivatives, integrals, and infinite series. Calculus plays a very important role in modern mathematics. It has two branches Differential Calculus and Integral Calculus. Both the branches play a vital role when we deal with Calculus. Calculus has lots of story from its beginning to present. The modern use of calculus began in Europe during the 17th century. Calculus have various applications where they are used, differential calculus persist:-velocity, acceleration optimization and Slope of the curve while integral calculus contain:-area, volume, center of mass, work, pressure and Arc Length. Calculus provides tools to solve many problems one of the problem is paradox which comes in limit and infinite series. Calculus was initially started to calculate or manipulate small type of quantities. If we see the fundamental theorem of calculus then we find that the differential and Integration operation are opposite to each other or we can say that inverse to each other. Calculus have so many applications, and is widely use in different fields wide variety of fields like computer science, statistics, economics business, physical science etc.