Arc Length

    The arc length of the curve    is found by using the integrand  .  The length of the catenary over the interval  [0,a] is given by the calculation  

    .

Exploration 3.

Or, we could first simplify the integrand, before using integration.

The arc length of the catenary over the interval  [0,a] is given by the calculation:

(c) John H. Mathews 2004