\(\left\{\frac{2}{3}\pi,\frac{2}{3}\pi\right\}\text{limites}\)
\(Datos\)
\(\overline{x}\ =r\cos\theta\)
\(\overline{y}=r\sin\theta\)
\(dl=rd\theta\)
\(r\ =300\ m\)
Solución
\(\overline{x}=\) ∫ \(\frac{\overline{x}\ dm}{integral\ dm}\) = ∫\(\frac{\overline{x}\ pdl}{integral\ pdl}\) = \(\frac{\overline{x}\ dl}{integral\ dl}\ \) ( formula esa sustituyendo para lo necesario)
\(\overline{x}\ =\) ∫ \(\frac{\overline{x\ }dl}{dl}\)= ∫\(\frac{r\cos\theta rd\theta}{integral\ R\ d\ teta}\)= \(R\)2 \(\int_{\frac{2pi}{3}}^{\frac{2pi}{3}}\cos\theta\ d\theta\)
\(r\ \sin\theta\ \int_{\frac{2pi}{3}}^{\frac{2pi}{3}}\)/\(\theta\int_{\frac{2pi}{3}}^{\frac{2pi}{3}}\)\(=\frac{r\ \left\{0.8+60.86\right\}}{\frac{4}{3}pi}=\ 380m\)
\(\left(\frac{1.732}{4.188}\right)=\) \(124\ M\)