Solución
X=2 cos\(\theta\)
Y= 2 sin\(\theta\)
dL= 2 d\(\theta\)
\(X\ =\ \frac{\int_{ }^{ }x\ dL}{\int_{ }^{ }dL}\ =\ \frac{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2\ \cos\theta\ 2\ d\theta}{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2d\theta}\ =\ \frac{4\sin\ \left|_{-\frac{\pi}{2}}^{\ \ \ \frac{\pi}{2\ }}\right|}{2\theta\left|\ _{-\frac{\pi}{2}}^{\ \ \frac{\pi}{2}}\right|}\)
\(=\frac{4}{\pi}\)
\(Y=\ \frac{\int_{ }^{ }Y\ dL}{\int_{ }^{ }dL}\ =\ \frac{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2\sin\theta\ 2d\theta}{\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}2d\theta}\ =\ \frac{4\left[-\cos\theta\right]}{2\theta\left|\ _{-\frac{\pi}{2}}^{\frac{\pi}{2}}\right|}=\frac{3}{\pi}\ \)
\(\theta\)