$x^{} y z$

$xyz$

$1-x- y$

$1-x-y$

$10-x^2-y^2$

$10-x^2-y^2$

$x^2$

$x^2$

$x$

$x$

$0$

$0$

$1$

$1$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{CenterOfMass}\right]\left(\,z\=..\, y\=..\,x\=..\,\mathrm{output}\=\mathrm{integral}\right)$

$\frac{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}{z}^{2}xy\ⅆz\ⅆy\ⅆx}{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}xyz\ⅆz\ⅆy\ⅆx}\,\frac{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}{y}^{2}xz\ⅆz\ⅆy\ⅆx}{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}xyz\ⅆz\ⅆy\ⅆx}\,\frac{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}{x}^{2}yz\ⅆz\ⅆy\ⅆx}{{\∫}_0^1{\∫}_{x^2}^x{\∫}_{1-x-y}^{10-x^2-y^2}xyz\ⅆz\ⅆy\ⅆx}$

$\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\left[\mathrm{CenterOfMass}\right]\left(\,z\=..\, y\=..\,x\=..\right)$

$\frac{3507743}{573782}\,\frac{332885}{573782}\,\frac{2494317}{3729583}$