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

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Chaz

Mathematics

15 December, 15:10

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

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Owen Villanueva · Answer 1

(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.