Let's assume the bridge cable is a parabola with equation y=x^2. Bust up the x-axis into n pieces where n is large.

Using n as an index variable instead of the above i, and setting the above n to 1000, we use a "Wolfram Alpha widget" to sum the series. The value computed is 1000 times the value we need.

Click here to link to the widget!

The *exact* value can be found with calculus.

The integral of

can be shown to be

Evaluate at 1 and 0 and subtract to get

2/8 (ln (5^(1/2) +2) + 2*5^(1/2)) = 1.4789

Click here to see the step by step derivation of the integral.