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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 ...
Download as PDF; Printable version; ... Bioche's rules; C. ... Fubini's theorem; Fundamental theorem of calculus; G. General Leibniz rule;
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.
For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus. [1] The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory . [ 2 ]
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 ...
This is known as the squeeze theorem. [ 1 ] [ 2 ] This applies even in the cases that f ( x ) and g ( x ) take on different values at c , or are discontinuous at c . Polynomials and functions of the form x a
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)