Length Command

Length[ <Vector> ]: Yields the length of the vector.
Length[ <Point> ]: Yields the length of the position vector of the given point.
Length[ <Function>, <Start x-Value>, <End x-Value> ]: Yields the length of the function graph in the given interval.; Example:
Length[2x, 0, 1] returns 2.23606797749979, about \sqrt{5}.

Length[ <Function>, <Start Point>, <End Point> ]: Yields the length of the function graph between the two points.; Note: If the given points do not lie on the function graph, their x‐coordinates are used to determine the interval.
Length[ <Curve>, <Start t-Value>, <End t-Value> ]: Yields the length of the curve between the two values of the parameter
Length[ <Curve>, <Start Point>, <End Point> ]: Yields the length of the curve between the two points that lie on the curve.
Length[ <List> ]: Yields the length of the list, which is the number of elements in the list.
Length[ <Text> ]: Yields the number of characters in the text.
Length[ <Locus> ]: Returns the number of points that the given locus is made up of. Use Perimeter[Locus] to get the length of the locus itself. For details see the article about First Command.
Length[ <Arc> ]: Returns the arc length (i.e. just the length of the curved section) of an arc or sector.

CAS Syntax

Length[ <Function>, <x-start>, <x-end> ]: Calculates the length of a function graph between the two points.; Example:
Length[2 x, 0, 1] yields \sqrt{5}.

Length[ <Function>, <Variable>, <Start Point>, <End Point> ]: Calculates the length of a function graph from Start Point to End Point.; Example:
Length[2 a, a, 0, 1] yields \sqrt{5}.

Note: