Example 1.  Find the catenary that goes through the origin and also passes through the two points  with  a = 10  and b = 6.

Solution 1.

Enter the formula for the catenary and determine the constant .  

Plot this solution.

The length of the catenary can be approximated numerically by using Simpson's rule.

The length of the catenary is easily computed using Mathematica's built in subroutine.

Remark. This could also be computed analytically.  Recall that

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Caution.  If you use then Mathematica will go into it's "special function" mode of operation and you will get Elliptic functions.

The formula Mathematica produces for will involve functions studied in first year calculus.

The following definite integral works.

Or you could use the formula

(c) John H. Mathews 2004