$\textsf{Find the center of mass of a thin plate of density

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

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

\begin{align*}\displaystyle

M&=\int_{0}^{\sqrt{2}}\int_{2-x^2}^{1}3 \, dy \, dx\\

&=3\int_{0}^{\sqrt{2}}\biggr[y\biggr]_{y=2-x^2}^{y=1}\, dx

=3\int_{0}^{\sqrt{2}}(x^2-1) \, dx

=3\biggr[\frac{x^3}{3}-x\biggr]_0^{\sqrt{2}}=\sqrt{2}\\

M_y&=\int_{0}^{\sqrt{2}}\int_{2-x^2}^{1} \, dy \, dx

=\int_{0}^{\sqrt{2}}\biggr[y\biggr]_{y=2-x^2}^{y=1}\, dx\\

&=\int_{0}^{\sqrt{2}}(x^2-1) \, dx = -\sqrt{2}\\

&\color{red}{\, \bar{x}=\frac{5}{14},\bar{y}=\frac{38}{35}}

\end{align*}

ok not doing something right

red is answer