Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integrals defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b.he term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function ƒ. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals. The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century. Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if ƒ is a continuous real-valued function defined on a closed interval [a, b], then, once an antiderivative F of ƒ is known, the definite integral of ƒ.These generalizations of integral first arose from the needs of physics, and they play an important role in the formulation of many physical laws, notably those of electrodynamics. There are many modern concepts of integration.
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