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 x-Value>, <End x-Value> ]

Yields the length of the curve between the two values.

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 a>, <Number t1>, <Number t2> ]

Calculates the length of a function graph from point a=t1 to point a=t2.

Example:

Length[2 a, a, 0, 1] yields \sqrt{5}.

Note:

See also Distance or Length tool.