Definition Of Integration Calculus Math

Given a function f of a real variable x and an interval a b of the real line the definite integral of f from a to b can be interpreted informally as the signed area of the region in the xy plane that is bounded by the graph of f the x axis and the vertical lines x a. Integration is the process of finding the definite or indefinite integral of a function. The process of finding a function given its derivative is called anti differentiation or integration.

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A definition of integration.

Definition of integration calculus math. Integral calculus is intimately related to differential calculus and together with it constitutes the foundation of mathematical analysis. Exhaustion method of. If f x f x we say f x is an anti derivative of f x. Both the integral calculus and the differential calculus are related to each other by the fundamental theorem of calculus.

Integration is one of the two main operations of calculus. Integration is a very important concept which is the inverse process of differentiation. Integral calculus is the branch of calculus where we study about integrals and their properties. The origin of integral calculus goes back to the early period of development of mathematics and it is related to the method of exhaustion developed by the mathematicians of ancient greece cf.

C is any fixed number and is called the constant of integration. Its inverse operation differentiation is the other. The integral is calculated to find the functions which will describe the area displacement volume that occurs due to a collection of small data which cannot be measured singularly. In a broad sense in calculus the idea of limit is used where algebra and geometry are implemented.

The integration denotes the summation of discrete data. Integration is the inverse of differentiation and is often called antidifferentiation. In this article let us discuss what is integral calculus why is it used for its types properties formulas examples and application of integral calculus in detail.