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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 ...
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
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 ]
Divergence theorem (vector calculus) Fermat's theorem (stationary points) (real analysis) Fraňková–Helly selection theorem (mathematical analysis) Froda's theorem (mathematical analysis) Fubini's theorem on differentiation (real analysis) Fundamental theorem of calculus ; Gauss theorem (vector calculus) Gradient theorem (vector calculus)
Print/export Download as PDF; Printable version; ... Pages in category "Theorems in calculus" The following 38 pages are in this category, out of 38 total.
The following three basic theorems on the interchange of limits are essentially equivalent: the interchange of a derivative and an integral (differentiation under the integral sign; i.e., Leibniz integral rule); the change of order of partial derivatives; the change of order of integration (integration under the integral sign; i.e., Fubini's ...
Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the most common antiderivatives.
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 ...
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