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%This is the driver srcript.

% This piece is a test. The answer should be close to 64.
N=1000; %Number of integration points
R=8;    %Radius

times=linspace(0,2*pi,N);
dt=times(2)-times(1);

%parametrization of the cycloid
x=R*(times-cos(times));
y=R*(1-sin(times));

%numerical calculation of derivatives
dx_dt=diff(x)/dt;
dy_dt=diff(y)/dt;...
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