Mathematics-Online lexicon: Properties of the Line Integral

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	Mathematics-Online lexicon:
	Properties of the Line Integral

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

The line integral $\int\limits_C f$ is linear in

and additive with respect to

$\displaystyle{\int\limits_C \alpha f + \beta g = \alpha \int\limits_C f + \beta \int\limits_C g}$
$\displaystyle{\int\limits_{C} f\,dC = \int\limits_{C_1} f+ \int\limits_{C_2} f}\,$ ,

for $C = C_1 \cup C_2$ where

and

are disjoint up to isolated points.

The integral is independent of the parametrization and particulary it does not depend on the orientation of .

(Authors: App/Höllig/Höfert)

automatically generated 8/ 4/2008