Y=0
\(x\frac{\int_1^{ }x\ \ dl}{\int_{1\ }^{ }x\ \ dl}\)
x=r cos \(\theta\)
Y=r sen \(\theta\)
dl= \(\sqrt{dx^2+dy^2\ }\)=\(r^2\) \(\left(sen^2\ \theta\ d\theta^2\right)+r^2\left(\cos^2\ d\theta^2\right)\)
dx=- r sen \(\theta\) =\(\sqrt{r^2d\theta^2\left(sen^2\theta+\cos^2\theta\right)}\)
dy= r cos \(\theta\) d\(\theta\) =r\(\theta\)
=\(\frac{\int_{\frac{-2\Pi}{3}}^{\frac{2\Pi}{3}}r\ \cos\theta\ d\theta\ }{\int_{\frac{-2\Pi}{3}}^{\frac{2\Pi}{3}}r\ d\theta}=\frac{r^2\ \int_{\frac{-2\Pi}{3}}^{\frac{2\Pi}{3}}\cos\theta\ d\theta}{r\int_{\frac{-2\Pi}{3}}^{\frac{-2\Pi}{3}}d\theta}\)
\(=\frac{r\ sen\ \theta\left|\frac{\frac{2\Pi}{3}}{\frac{-2\Pi}{3}}\right|}{\theta\left|\frac{\frac{2\Pi}{3}}{\frac{-2\Pi}{3}}\right|}=\frac{r\left|0.0866+0.866\right|}{\frac{4\Pi}{3}}=\frac{300mm\left|1.732\right|}{4.189}=124\ mm\)
X=\(\frac{\int_2^{ }x\ dl}{\int_{_2}^{ }\ dl}=\int_{\frac{-\Pi}{2}}^{\frac{\Pi}{2}}r\ \cos\theta\ r\theta\)
X= r cos \(\theta\)
dl= r d \(\theta\)
\(\frac{r\ sen\ \theta\left|\frac{\frac{\Pi}{2}}{\frac{-\Pi}{2}}\right|}{\theta\left|\frac{\frac{\Pi}{2}}{\frac{-\Pi}{2}}\right|}=\frac{r\left[1+1\right]}{\Pi}=\frac{2\left(2\right)}{\Pi}=\frac{4}{2}=1.25\)
(1) .\(\Sigma\ \ fx\) Bx=11b
2.- \(\Sigma\ \ fy\) Ax= 11b
3.- \(\Sigma\ \ ma\) Ay= \(\Pi\) lb