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Math · Calculus
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A region R plotted in the xy-plane with the equations

x(t)=cos(t)(1-cos(t))   and y(t)=sin(t)(1-cos(t))

as t goes from 0 to 2pi

Use the Gauss-Green formula to calculate the centroid of this region

Clear[x, y, t]; x(t_] = cos[t] (1 - cos(t)); yIt] Sin[t] (1 Cos[t]); Rplot - ParametricPlot [(x[t], y[t]), {t, θ, 2 Pi), (x, yJ, Epilog - Text[R, f-0.8, 0.53]] PlotRange-) All, Plotstyle-) {{Red, Thickness[0.01])), Axe s Label-> 0.5 0 -0.5 -1

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