Finding the Length of the Cable

In[14]:=

  Integrate[Evaluate[Sqrt[1 + D[catenary[x,t2], x]^2]],
  											{x,-50,50}]

  On::none: Message SeriesData::csa not found.

  General::intinit: Loading integration packages -- please wait.

Out[14]=

                                          2
  Integrate[Sqrt[1 + 1. Sinh[0.00789687 x] ], {x, -50, 50}]

Mathematica cannot integrate this function exactly. We must approximate the integral using NIntegrate. This command uses an algorithm called Gauss quadrature--but that is the subject of another lesson.

In[15]:=

  NIntegrate[Evaluate[Sqrt[1 + D[catenary[x,t2], x]^2]],
  											{x,-50,50}]

Out[15]=

  102.619

So you will need an extra 2.6 meters of cable to span 100 meters.

Reference: This problem was adapted from Cheney and Kincaid, Introduction to Numerical Methods.

Up to An Example: The Length of a Suspended Cable