- #1

karush

Gold Member

MHB

- 3,269

- 5

$\textsf{ $\delta=3$ bounded by the lines $x=0, y=x$, and the parabola

$y=2-x^2$ in the $Q1$}$

$\begin{array}{llcr}\displaystyle

&\textit{Mass}\\

&&\displaystyle M=\iint\limits_{R}\delta \, dA\\

&\textit{First Moments}\\

&&\displaystyle M_y=\iint\limits_{R}x\delta \, dA

&\displaystyle M_x=\iint\limits_{R}y\delta \, dA\\

&\textit{Center of mass}\\

&&\displaystyle\bar{x}=\displaystyle\frac{M_y}{M},

\displaystyle\bar{y}=\displaystyle\frac{M_x}{M}\\

\\

&&\color{red}

{\displaystyle \, \bar{x}=\frac{5}{14},

\bar{y}=\displaystyle\frac{38}{35}}\\

\end{array}$ok I just barely had to time to post this

equations are just from reference

red is answer