\(x^{-=}\frac{\int_A^{ }x^{\sim\ }dA\ \ }{\int_A^{ }dA}\)\(y^{-=}\frac{\int_A^{ }y^{\sim}dA}{\int_A^{ }dA}\)         
\(x^{\sim}=R\cos\theta\)
\(y^{\sim}=R\sin\theta\)
\(dA=Rd\theta\)
\(x^-\)\(-\frac{2\pi}{3}a\ \frac{2\pi}{3}\)\(x^-\)
\(x^{-=}\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}R^2\cos\theta d\theta}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rd\theta}\)
 
\(x^-=\frac{R\left(\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}\cos\theta\right)}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}d\theta}\)
\(\theta\)
\(x^-=\frac{R\left[\left(\sin\left(\frac{2\pi}{3}\right)-sen\left(-\frac{2\pi}{3}\right)\right)\right]}{\left(\frac{2\pi}{3}+\frac{2\pi}{3}\right)}\)
\(x^-=\frac{\left(\left(0.3\right)\left(1.732\right)\right)}{4.189}=0.124\ m\)       
\(x^-=0.124\ m\) 
   
\(y^-\)
\(y^-=\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}R^2\sin\theta d\theta}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rd\theta}\)
\(y^-=\frac{R\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}\sin d\theta}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}d\theta}\)
\(\theta\)
\(y^-=\frac{\left[\left(-\cos\left(\frac{2\pi}{3}\right)+\cos\left(-\frac{2\pi}{3}\right)\right)\right]}{\left(\frac{2\pi}{3}+\frac{2\pi}{3}\right)}\)
\(y^-=\frac{\left(\left(0.3\right)\left(0\right)\right)}{4.189}=0\)            
\(y^-=0\)

\(x^-\)