(a) Find the area of the region bounded by the x axis and one arch of...

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(a) Find the area of the region bounded by the x axis and one arch of the cycloid

x = a(0 = sin0), y = a(1 = cos 0) (0  0  2)

where a is a positive constant.

(b) Show that the radius of curvature of the cycloid defined in (a) at the point O is given by

p = 22a(1-cos)/

What is the maximum value of ρ?

(c) Discuss the nature of the radius of curvature when θ = 0 or θ = 2π.

(d) Determine the length of one arch of the cycloid.

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