Changes

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''' 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.

The common notation for a line integral, taken along a line expressed as "contour C," of a vector function ''f'' is:

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>

 

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

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

[[Category:calculus]]

[[Category:calculus]]

[[Category:mathematics]]

[[Category:mathematics]]