Solución 
\(x=2\cos\theta\)
\(y=2\sin\theta\)
\(dl=2d\theta\)
\(x=\frac{\int_.^.xdl}{\int_.^.dl}=\frac{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2\cos\theta2d\theta}{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2d\theta}=\frac{4\sin\left|_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}{2\theta\left|_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}=\frac{4}{\pi}\)
\(y=\frac{\int_.^.ydl}{\int_,^,dl}=\frac{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2\sin\theta2d\theta}{\int_{-\frac{\pi}{2}}^{\frac{2}{\pi}}2d\theta}=\frac{4\left[-\cos\right]_{-\frac{\pi}{2}}^{\frac{\pi}{2}}}{2\theta\left|_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}=\frac{3}{\pi}\)
\(x=\frac{\int_.^.xdl}{\int_.^.dl}=\frac{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2\cos\theta2d\theta}{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2d\theta}=\frac{4\sin\left|_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}{2\theta\left|_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}=\frac{4}{\pi}\)