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example
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''' 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} \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>
''Example'': The work done on a particle to move it from one point to another is the line integral of the force on the particle along the curve of its motion:
:<math>\int_\mathbf{C} \vec{F}(\vec{r}) \cdot d\vec{r}</math>
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 line.
[[Category:vector analysis]]
[[Category:vector analysis]]
[[Category:calculus]]
[[Category:calculus]]
[[Category:mathematics]]
[[Category:mathematics]]