Question

I'm confused by the integration behind a very basic Divergence Theorem problem and can't figure out why yet. Posted below momentarily.

Answer 1

\[F = (y-x)i+(z-y)j+(y-x)k,\]

The region involved is the cube bounded by the planes \[x, \ y,\ z\ =\pm1\]

Answer 2

What I'm confused about is intuitively I can imagine the flux through this region being 0-which it is-but in the integration, I'm somewhere making a very basic mistake giving me nonzero values. Integration setup in a moment.

Answer 3

(LaTeX issues, one sec)

Answer 4

\[\int\limits_{-1}^{1}\int\limits_{-1}^{1}\int\limits_{-1}^{1}(-2)dxdydz\]Something already has to be wrong here at this tage. The way I got the -2 was

Answer 5

\[\triangledown \cdot F=\frac{\partial M}{\partial x}+\frac{\partial N}{\partial y}+\frac{\partial P}{\partial z}=(-1)i+(-1)j\]

Answer 6

Summing those two giving the integrand.

Answer 7

why do you think the flux out of cube will be 0 ?

Answer 8

\[\int\limits_{-1}^{1}\int\limits_{-1}^{1}\int\limits_{-1}^{1}-2 \ dx \ dy \ dz=\int\limits_{-1}^{1}\int\limits_{-1}^{1}\]

WHOOP nevermind, I was reading the wrong section of the answers, nevermind, the answrer is not zero and I was doing things right. Lol, sorry.