Question

This website has the wrong formula for center of mass of thin planar sheet. the website says that
y* = integral y (x2-x1) / Area

Answer 1

http://www.intmath.com/applications-integration/5-centroid-area.php

Answer 2

the My part,

Answer 3

\[\vec{r}_{CM}=\frac{1}{S}\iint\limits_S\vec{r}\,dS\quad;\quad \vec{r}=x\vec{i}+y\vec{j}\quad\quad,\quad dS=dxdy\]\[\vec{r}_{CM}=\frac{1}{S}\iint\limits_S(x\vec{i}+y\vec{j})\,dxdy=\]\[=\frac{\vec{i}}{S}\iint\limits_Sx\,dxdy+\frac{\vec{j}}{S}\iint\limits_Sy\,dxdy\quad,\quad S=\iint\limits_S dxdy\]