(Solved): The quarter-circle shown below has radius \( R \). What is the \( (x, y) \) p ...

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The quarter-circle shown below has radius \( R \). What is the \( (x, y) \) position of the centroid? \[ \begin{array}{l} \left(\frac{R}{3}, \frac{R}{3}\right) \\ \left(\frac{3 \pi}{4 R}, \frac{3 \pi}{4 R}\right) \\ \left(\frac{4 R}{3 \pi}, \frac{R}{3}\right) \\ (R, R) \\ \left(\frac{4 R}{3 \pi}, \frac{4 R}{3 \pi}\right) \end{array} \]