(Solved):
Here's region \( \mathrm{R} \) plotted in the \( x y-p l a n e: \) \[ \begin{array}{l} f(t)=\cos ( ...
Here's region \( \mathrm{R} \) plotted in the \( x y-p l a n e: \) \[ \begin{array}{l} f(t)=\cos (t)(1-\cos [t]) \\ g(t)=\sin (t)(1-\cos \lceil t]) \end{array} \] \( -2.5 \ldots 0.8= \) left...right \( -1.5 \ldots 1.5= \) bottom ...top cropping ( \( ? \) Graph Building Blocks in Curve at \( (f[t], g[t]) \) where \( t=0 \ldots 2 \pi \) with a \( \quad \) line, colored Fancy dudes from Ivy League schools say that this is the cardioid described in \( \pi \) coordinates by the polar equation \( \mathrm{r}(\mathrm{t})=1-\cos (\mathrm{t}) \). Use the Gauss-Green formula to help you to calculate the centroid of this region.