The $B\subset \mathbb R ^3$ is the pyramid with the corner points $P(0,0,0),P(2,0,0),P(0,2,0)$ and $P(0,0,1)$. The area $B$ is through the smooth surface $F$ limited. Calculate the flow of a vector field $a=(x_3-x_1^2,2x_1-x_3,x_2-x_1)$ through $F$ using divergence theorem.
I did it like this:
$div a=-2x_1$
$\int_{0}^{2} \! \int_{0}^{2} \!\int_{0}^{1} \! -2x_1 \, dx_3 \, dx_2 \, dx_1 =-8$
Can someone say if this is good or not?