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The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...
In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]
Bioche's rules; C. Cantor's intersection theorem; Chain rule; D. Darboux's theorem (analysis) ... Fubini's theorem; Fundamental theorem of calculus; G. General ...
These rules are given in many books, both on elementary and advanced calculus, in pure and applied mathematics. Those in this article (in addition to the above references) can be found in: Mathematical Handbook of Formulas and Tables (3rd edition), S. Lipschutz, M.R. Spiegel, J. Liu, Schaum's Outline Series, 2009, ISBN 978-0-07-154855-7.
Simplest rules Sum rule in integration; Constant factor rule in integration; Linearity of integration; Arbitrary constant of integration; Cavalieri's quadrature formula; Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the ...
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function. The first part of the theorem, sometimes called the first fundamental theorem of calculus , states that one of the antiderivatives (also called indefinite integral ), say F , of some function f may be ...
Fundamental theorem; ... Rolle's theorem; Mean value theorem; Inverse function theorem; Differential. ... Calculus is used to give a brief outline of calculus topics ...
Fundamental theorem of algebra (complex analysis) Fundamental theorem of arbitrage-free pricing (financial mathematics) Fundamental theorem of arithmetic (number theory) Fundamental theorem of calculus ; Fundamental theorem on homomorphisms (abstract algebra) Fundamental theorems of welfare economics ; Furry's theorem (quantum field theory)