Show that the length of the arc of the cycloid, \( \left.\begin{array}{l}x=a(\theta+\sin \theta)...
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0Show that the length of the arc of the cycloid, \( \left.\begin{array}{l}x=a(\theta+\sin \theta) \text {, } \\ y=a(1-\cos \theta),\end{array}\right\} \) between the points for which \( \theta=0 \) and \( \theta=2 \psi \), is \( s=4 a \sin \psi \).
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