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three common techniques are available
:<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:
*[[parameterization]], which reduces multiple variables to only one (typically "t"), first for the underlying curve and then for the vector function
*for a closed curve (a loop), [[Green's Theorem]] converts the line integral around the lop into a double integral over the region inside
*for a [[conservative field]], which are path-independent, find the exact differentials at the end points and calculate the difference
''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:
''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: