Use one of the formulas below to find the area under one arch of the cycloid x = t − sin(t), y = 1 − cos(t). a = c x dy = − c y dx = 1 2 c x dy − y

(Green's Theorem" The area is bound by the x-axis on the bottom part from x = 0 to x = 2Ď€, and by the cycloid on the top. C = the bounding curve Csub1 = the x-axis part of C Csub2 =the cycloid part. You will take an integeral 2 x the Area will end up being the integral from 2pi to 0 of cos(t)dt with is 6pi So 2 x Area = 6pi so the area = 3pi.