The Humber Bridge, located in the United Kingdom and opened in 1981, has a main span of about 1400 meters. Each of its towers has a height of about 155 meters. Use these dimensions, the integral in Exercise 67, and the integration capabilities of a graphing utility to approximate the length of a parabolic cable along the main span.

Data from in Exercises 67

A cable for a suspension bridge has the shape of a parabola with equation y = kx². Let h represent the height of the cable from its lowest point to its highest point and let 2w represent the total span of the bridge (see figure). Show that the length C of the cable is given by

Transcribed Image Text:

C = 2 W 0 1 + (4h²/w4)x² dx.