Length Command

Length[ <Object> ]

Yields the length of the object.

Examples:

• Length[ <Vector> ] yields the length of the vector.
• Length[ <Point> ] yields the length of the position vector of the given point.
• 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.

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.

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:

See also Distance or Length tool.