Triple integral bounds 
*

*Let $W$ be the region bounded by the planes
$x = 0$, $y = 0$, $z = 0$, $x + y = 1$, and $z = x + y$.

*$(x^2 + y^2 + z^2)\, \mathrm dx\, \mathrm dy\, \mathrm dz$; $W$ is the region bounded by $x + y + z = a$ (where $a > 0$), $x = 0$, $y = 0$, and $z = 0$.
$x,y,z$ being $0$ is throwing me off because I'm not sure how to graph it and get a bounded area; it seems like it would be infinite to me. What would the bounds for the triple integrals be?

1) give you nothing to integrate.  But we can still find the limits
$z = 0$ lower limit for $z$
$z = x+y$ upper limit for $z$
$y = 0$ lower limit for $y$
$y = 1-x$ upper limit for $y$
$x = 0$ lower limit for $x$
$x = 1$ upper limit for $x$
For the last one, because that is where $y = 0$ intersects $x+y = 1$
2)
$\int_0^a\int_0^{a-x}\int_0^{a-x-y} x^2 + y^2 + z^2 \;dz\;dy\;dx$
