Catenary Curves A chain (or cable) of uniform density that is suspended between two points, as shown in the figure, hangs in the shape of a curve called a catenary with equation y = a cosh(x/a).

(a) Find the arc length of the catenary y = a cosh(x/a) on the interval [c, d].

(b) Show that on any interval fc, d, the ratio of the area under the catenary to its arc length is a.

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