1. divergence theorem

Can someone just help me set up the following integrals?

For the region R in the first octant bounded above by the plane x+y+z=1 and the surface S which is the boundary of this region, calculate for the vector valued function F=(x^2+y^2)i+(y^2+z^2)j+(z^2+x^2)k:

(i) triple integral (div F) dV
(ii) double integral (F*n) dS where n is the outward pointing unit normal.

Thank you for any help.

Can someone just help me set up the following integrals?

For the region R in the first octant bounded above by the plane x+y+z=1 and the surface S which is the boundary of this region, calculate for the vector valued function F=(x^2+y^2)i+(y^2+z^2)j+(z^2+x^2)k:

(i) triple integral (div F) dV
(ii) double integral (F*n) dS where n is the outward pointing unit normal.
First I like to mention that by Gauss' theorem,
$\oint _S \oint \bold{F}\cdot \bold{n} dS=\int \int_R \int \mbox{ div }\bold{F} dV$
Thus, all we need to do if find,
$\int \int_R \int \mbox{ div }\bold{F} dV$
Now,
$\mbox{div }\bold{F}=2x+2y+2z=2x+2y+2z$
Thus, by Fubini's theorem, (details omitted)
$\int_0^1 \int_0^{1-x} \int_0^{1-x-y} 2x+2y+2z dz\, dy\, dx$

3. Yeah, so my assignment paper has (i) and (ii) as two different questions and answers. Is there a difference?

By Gauss' Theorem (divergence theorem), they appear to be the same?