Line integral

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:

$\int _{\mathbf {C} }\langle {\vec {f}}({\vec {s}}),d{\vec {s}}\rangle$