exo7 4384

$D=\{0\le x\le1, 0\le y\le1, 0\le z\le1\}$,

$f(x,y,z)=\frac1{(x+y+z+1)^3}$.

$D=\{x^2+y^2+z^2 \le R^2\}$,

$f(x,y,z)=\frac1{\sqrt{a^2-x^2-y^2-z^2}} \quad(a>R>0)$.

$D=\{x\ge0, y\ge0, z\ge0, x+y+z\le1\}$,

$f(x,y,z)=xyz$.

$D=\{x\ge0, y\ge0, z\ge0, x+y+z\le1\}$,

$f(x,y,z)=\frac1{(x+y+z+1)^2}$.

$D=\{x^2+y^2\le R^2, 0\le z\le a\}$,

$f(x,y,z)=x^3+y^3+z^3-3z(x^2+y^2)$.

$D=\{x^2+y^2\le z^2, 0\le z\le 1\}$,

$f(x,y,z)=\frac z{(x^2+y^2+1)^2}$.

$D=\left\{\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} \le 1\right\}$,

$f(x,y,z)=x^2+y^2$.