영역 $D= \left \{(x, y) \vert 1 \leq x ^ {2} +y ^ {2} \leq 4, x \geq 0, y \geq 0 \right \}$ 의 무게중심 (centroid, center of mass)의 좌표는?

• ①$\displaystyle \left (\frac{31} {9 \pi}, \frac{31} {9 \pi} \right)$
• ②$\displaystyle \left (\frac{32} {9 \pi}, \frac{32} {9 \pi} \right)$
• ③$\displaystyle \left (\frac{28} {9 \pi}, \frac{28} {9 \pi} \right)$
• ④$\displaystyle \left (\frac{29} {9 \pi}, \frac{29} {9 \pi} \right)$
• ⑤$\displaystyle \left (\frac{10} {3 \pi}, \frac{10} {3 \pi} \right)$