First moment of area ($M_x={\iint }_{R}ydA,M_y={\iint }_{R}xdA$)

For a planar region $R$ of finite positive area $A$, its first moments of area about the coordinate axes are the displayed double integrals, provided they exist. Its centroid is $(\overline{x},\overline{y})=(M_y/A,M_x/A)$. This follows by applying the definition $\overline{\mathbf{r}}=A^{-1}{\iint }_R\mathbf{r}dA$ to each component. The subscript indicates the axis about which the moment is taken: the first moment about the $x$-axis weights by $y$, not $x$.