# Length Command

##### Command Categories (All commands)

Length[ <Vector> ]
Yields the length of the vector.
Length[ <Point A> ]
Yields the length of the position vector of the given point .
Length[ <Function>, <Number x1>, <Number x2> ]
Yields the length of the function graph in the interval [x1, x2].
Example:
Length[2x, 0, 1] returns 2.23606797749979, about \sqrt{5}.
Length[ <Function>, <Point A>, <Point B> ]
Yields the length of the function graph between the two points A and B.
Note: If the given points do not lie on the function graph, their x‐coordinates are used to determine the interval.
Length[ <Curve>, <Number t1>, <Number t2> ]
Yields the length of the curve between the parameter values t1 and t2.
Length[ <Curve c>,< Point A>, <Point B> ]
Yields the length of curve c between two points A and B 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.
Note:

## CAS Syntax

Length[ <Function>, <Number t1>, <Number t2> ]
Calculates the length of a function graph from point x=t1 to point x=t2.
Example:
Length[2x, 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[2a, a, 0, 1] yields \sqrt{5}.
Length[ <Segment> ]
Yields the length of the segment.
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