Ecuaciones:
\(\overline{x}=\frac{\int_L^{ }xdL}{\int_L^{ }dL}\)
\(\overline{y}=\frac{\int_L^{ }ydL}{\int_L^{ }dL}\)
\(x=R\cos\theta\)
\(y=R\sin\theta\)
\(dL=Rd\theta\)
Se sustituyen "\(x\)" ,"\(y\)" y "\(dL\)" en las ecuaciones \(\overline{x}\ \)\(\overline{y}\)
\(\overline{x}=\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}(R\cos⁡θ)Rdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rdθ}\ \)
\(\overline{x}=\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}R^2\cos⁡θdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rdθ}\)
\(\overline{x}=\frac{R\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}\cos⁡θdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}dθ}\)
\(\overline{y}=\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}(Rc\sin⁡θ)Rdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rdθ}\ \)
\(\overline{y}=\frac{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}R^2\sin⁡θdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}Rdθ}\)
\(\overline{y}=\frac{R\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}\sin⁡θdθ}{\int_{-\frac{2\pi}{3}}^{\frac{2\pi}{3}}dθ}\)
Se integran las ecuaciones y se sustituye \(\frac{2\pi}{3}\)\(-\frac{2\pi}{3}\):
\(\)\(\overline{x}=\frac{R\left(\sinθ\right)\ \frac{2\pi/3}{-2\pi/3}}{\left(θ\right)\ \frac{2\pi/3}{-2\pi/3}}\)
\(\frac{\left(300\right)\left(1.732\right)}{\frac{2\pi}{3}+\frac{2\pi}{3}}=\frac{\left(300\right)\left(1.732\right)}{\frac{2\pi}{3}+\frac{2\pi}{3}}=\frac{\left(300\right)\left(1.732\right)}{\frac{4\pi}{3}}=\frac{3\left(1.732\right)\left(300\right)}{4\pi}=124.04mm\)