Category:Arc Length

This category contains results about Arc Length.
Definitions specific to this category can be found in Definitions/Arc Length.

Let $y = \map f x$ be a real function which is:

continuous on the closed interval $\closedint a b$

and:

continuously differentiable on the open interval $\openint a b$.

Definition $1$

The arc length $s$ of $f$ between $a$ and $b$ is defined as:

$\ds s := \int_a^b \sqrt {1 + \paren {\frac {\d y} {\d x} }^2} \rd x$

Definition $2$

The length of the arc of a curve is defined as the limit of the length of a polygonal line inscribed within the curve as the maximum length of the chords which form that polygonal line tends to zero.