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Integral Calculus is a sub-branch of infinitesimal calculus concerned with the theory and applications of integrals. Its deals with topics related to integration. It is a powerful tool in science, engineering, and mathematicians. It is used for calculations of lengths, areas, volumes and central points. The process of finding the function from its derivative is called anti-derivative which is also referred to as Integration. In this process, the result obtained after the integration is called the integral. Integration is the reverse operation of differentiation. Integral and integration hold many properties and the study of these properties in the branch of mathematics is called Integral Calculus. The fundamental theorem of integral calculus (as well as differential calculus) were developed in the works of René Descartes, Archimedes, Gottfried Leibniz, Issac Barrow, and Isaac Newton at the end of the 17th century. Differential Calculus and Integral calculus are two branches of calculus which are connected by the fundamental theorem, which shows how a definite integral is calculated by using its antiderivative (a function whose rate of change, or derivative, equals the function being integrated). In Integral calculus, area under a curve is studied where as in differential calculus the derivative equation is used to describe the rate of change of a function. Integral calculus deals with the derivation of formulas for finding antiderivatives. For further study on this topic we are invite you to take a look at integral calculus books.

Integral Calculus Integral Calculus is the branch of calculus in which we study integrals and their properties. Integral calculus deals with total size or value, such as lengths, areas, and volumes While differential calculus focuses on rates of change, such as slopes of tangent lines and velocities, integral calculus deals with total size or value. Both the integral and differential calculus are related to each other by the fundamental theorem of calculus. Integration Integral Calculus helps us to find the anti-derivatives of a function. These anti-derivatives are also called the integrals of the function. The process of finding the anti-derivative of a function is called integration. Integration is the inverse process of differentiation. Integration can be classified into two different categories, namely, Definite Integral and Indefinite Integral Definite Integral An integral is said to be definite integral if it has upper and lower limits. The definite integral generalizes the concept of the area under a curve, it has start and end values: in other words there is an interval [a, b]. The number “a” that is at the bottom of the integral sign is called the lower limit of the integral and the number “b” at the top of the integral sign is called the upper limit of the integral. Also, despite the fact that a and b were given as an interval the lower limit does not necessarily need to be smaller than the upper limit. "a" and "b" said to be the interval of integration. A definite Integral is also called a Riemann Integral when it is bound to lie on the real line. b ? f(x) dx a -- Indefinite Integral A simple integral is said to be Indefinite integral if it has no upper and lower limits. The process of finding the indefinite integral is called integration or integrating and, sometimes called an antiderivative. Integration is the reverse process of differentiation. It is visually represented as an integral symbol ?, a function f(x), and then a dx at the end. ? f(x) dx Because the derivative of a constant is zero, the indefinite integral is not unique.

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Free Integral Calculus Books