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ArcLengthFactor

ArcLengthFactor[{f1, f2, f3}, t]
gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f1, f2, f3} with respect to the parameter t in the default coordinate system.
ArcLengthFactor[{f1, f2, f3}, t, coordsys]
gives the derivative of the arc length of a curve in the coordinate system coordsys.
  • The parametrized curve coordinates {f1, f2, f3} should be given in coordsys, if specified, or the default coordinate system otherwise.
  • If the parametrized curve coordinates {f1, f2, f3} are not given, the default coordinate variables for coordsys are used.
  • Integrate[ArcLengthFactor[{f1, f2, f3}, t], {t, t1, t2}] gives the length of the arc described by {f1, f2, f3} from t1 to t2.