Changes

:<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>

The multiple variables in a line integral pose difficulties in solving them.  Three common techniques are available:

The multiple variables in a line integral pose difficulties in solving it.  Three common techniques are available:

*[[parameterization]], which reduces multiple variables to only one (typically "t"), first for the underlying curve and then for the vector function

*[[parameterization]], which reduces multiple variables to only one (typically "t"), first for the underlying curve and then for the vector function

A '''line integral''' of a non-vector function is the summation of the values taken by the function (its integral) over the domain defined by the curve.  Put another way, the line integral is the area under the function and along the curve.  The familiar, basic integral is simply the line-integral using the x-axis as the curve.

A '''line integral''' of a non-vector function is the summation of the values taken by the function (its integral) over the domain defined by the curve.  Put another way, the line integral is the area under the function and along the curve.  The familiar, basic integral is simply the line-integral using the x-axis as the curve.

[[Category:vector analysis]]

[[Category:Vector Analysis]]

[[Category:calculus]]

[[Category:Calculus]]

[[Category:mathematics]]

[[Category:Mathematics]]