Mathematics-Online lexicon: Fundamental Theorem of Calculus

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	Mathematics-Online lexicon:
	Fundamental Theorem of Calculus

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

is a primitive of a continuous function

$\left(f=F^\prime\right)$ , then it is

$\displaystyle \int_a^b f(x)\,dx = F(b) - F(a)$

which is commonly abbreviated as

$\displaystyle \int_a^b f = \left[ F \right]_a^b \,.$

A definite integral can thus be calculated as the difference of the primitive's values at the interval's boundary points.

(Authors: Höllig/Hörner/Abele)

Examples:

automatically generated 4/ 8/2008