Line integrals

Suppose a space curve

is defined by component functions

for values of

from

. Moreover, suppose that the points of

lie in the domain of a function

. We wish to compute the line integral of

over

. We write this as

where the differential

represents change along path

. To compute, we can express this integral in terms of the parameter

. In the above expression,

is replaced by

, where

Developed for use with Thomas' Calculus, published by Pearson.

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