Difference between revisions of "Line integral"

Revision as of 18:59, December 26, 2009

A line integral of a vector function f along a line or curve segment C is the following (all three formulations are equivalent);

<math>\int_\mathbf{C} \vec{f}(\vec{s}) \cdot d\vec{s}</math>

<math>\int_\mathbf{C} f_1s_1 dx + f_2s_2 dy + f_3s_3 dz</math>

<math>\int_\mathbf{C} \langle \vec{f}(\vec{s}), d\vec{s} \rangle</math>

@@ Line 1: / Line 1: @@
-A '''line integral''' is the area under a function along a specified curve.  An ordinary or Riemann [[integral]] is a line integral using the x-axis as the line and bound by a given interval on the x-axis.
+A '''line integral''' of a vector function ''f'' along a line or curve segment ''C'' is the following (all three formulations are equivalent);
-A '''line integral''' is typically evaluated for the values taken by a three-dimensional vector field along a line or curve segment ''C''.  In this common use the line integral of a vector function ''f'' along ''C'' is the following (all three formulations are equivalent);
 :<math>\int_\mathbf{C} \vec{f}(\vec{s}) \cdot d\vec{s}</math>