\(x=r\ \cos\ \theta\)
\(y=r\ \sin\ \theta\)
\(dL=rd\theta\)
\(x=\frac{\int_1^1xdm}{\int_1^1dm}=\frac{\int_1^1x\gamma dL}{\int_1^1\gamma dL}=\frac{\int_1^1x\gamma dL}{\int_1^1dL}\ \)
\(\frac{\int_1^1r\ \cos\ \theta\ r\ d\theta}{\int_1^1r\ d\theta}=\frac{r^2\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}\cos\ \theta\ d\theta}{r\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}d\theta}=\frac{r\ \sin\ \theta\ \frac{\frac{2\pi}{3}}{-\frac{2\pi}{3}}}{\theta\frac{\frac{2\pi}{3}}{-\frac{2\pi}{3}}}\)
\(=\ \frac{\left[0.86\ +\ 0.86\right]}{\frac{4}{3}\pi}=300m\ \left(\frac{1.732}{4.188}\right)=124\ mm\) (centro de masa de la figura \ref{665022})

Problema No 2.