Between the two towers of a suspension bridge that are 2 kilometres apart, each of the two main cables has the shape of the parabola y =x2 (units are in kilometre) and hanging from the same height of the towers. Meanwhile, the vertical cables hanging from the main cable to the horizontal roadway are closely and equally spaced. a) State the definite integral which gives the length of each main cable between the two towers. b) Compute the average length (to the nearest meter) of the vertical cables.

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