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To compute the integral, we set n to its value and use the reduction formula to express it in terms of the (n – 1) or (n – 2) integral. The lower index integral can be used to calculate the higher index ones; the process is continued repeatedly until we reach a point where the function to be integrated can be computed, usually when its index is 0 or 1.
Method of Fluxions (Latin: De Methodis Serierum et Fluxionum) [1] is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736. [2]
The development of analytical geometry and rigorous integral calculus in the 17th-19th centuries subsumed the method of exhaustion so that it is no longer explicitly used to solve problems. An important alternative approach was Cavalieri's principle , also termed the method of indivisibles which eventually evolved into the infinitesimal ...
5th century BC - Democritus finds the volume of cone is 1/3 of volume of cylinder, 4th century BC - Eudoxus of Cnidus develops the method of exhaustion, 3rd century BC - Archimedes displays geometric series in The Quadrature of the Parabola. Archimedes also discovers a method which is similar to differential calculus. [1]
Integral calculus is the study of the definitions, properties, and applications of two related concepts, the indefinite integral and the definite integral. The process of finding the value of an integral is called integration. [47]: 508 The indefinite integral, also known as the antiderivative, is the inverse operation to the derivative.
The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Martin's Press which provides an introduction; three preliminary chapters explaining functions, limits, and derivatives; an appendix of recreational calculus problems; and notes for modern readers. [1]