Evaluate the triple integral $\iiint (x^2+y^2+z^2)\,dx\,dy\,dz$ I have to evaluate this integral. It is enough for me to know the correct limits to integration.
$$ \iiint_W  (x^2 + y^2 + z^2) \,\mathrm dx\,\mathrm dy\,\mathrm dz$$
Conditions: 
$$x\ge 0,\quad y \ge 0 ,\quad z \ge 0,\quad 0 \le x + y + z \le a,\quad (a>0)$$
My ideas:
As I have 
$0 \le x + y + z \le a$,
I can say that $$0 \le x + y + z$$
$$x \le - z - y $$
so my limits to integration could be: 
$$\int _{ z }^{ a }{  } \int _{ -z-y }^{ y }{  } \int _{ 0 }^{ -z-y }{ (x^2 + y^ 2+ z^ 2) \,\mathrm dx\,\mathrm dy\,\mathrm dz } $$
Can somebody help/correct me?

first for $x$:
$$0<x+y+z<a$$ implies $$0<x<a-y-z$$
Now x is dead :-) hence $$0<y+z<a$$ implies $$0<y<a-z$$ 
Now y is also dead hence $$0<z<a$$ therefore $$\int_0^a \int_0^{a-z}\int_0^{a-y-z}(x^2+y^2+z^2)dxdydz$$
