# Thread: Center of mass

1. ## Center of mass

https://imgur.com/a/KZOxs

Can someone let me know why I got this wrong?

2. ## Re: Center of mass

\begin{align*} &M = \displaystyle \int_0^{\frac{\pi}{2}}~2\sin(2x)~dx = \\ \\ &\left . -\cos(2x) \right |_0^{\frac \pi 2} = \\ \\ &-(-1 - 1) = 2 \end{align*}

\begin{align*} &M_x = \displaystyle \int_0^{\frac \pi 2}\int_0^{2\sin(2x)}~y~dy~dx = \\ \\ &\displaystyle \int_0^{\frac \pi 2}~\left(\left .\dfrac{y^2}{2}~\right|_0^{2\sin(2x)}\right) ~dx = \\ \\ &\displaystyle \int_0^{\frac \pi 2}~2\sin^2(2x)~dx = \dfrac{\pi}{2} \end{align*}

$\overline{y} = \dfrac{M_x}{M} = \dfrac{\frac \pi 2}{2} = \dfrac \pi 4$