
Flux integrals
Compute the flux of the field $\displaystyle F(x,y,z)=(x,y,z)$ through the disc defined by $\displaystyle x^2+y^2\le25,$ $\displaystyle z=12$ and oriented according the superior norm $\displaystyle \vec k.$
I don't get when it says "oriented according the superior norm $\displaystyle \vec k.$"
By applying the divergence theorem I get $\displaystyle 3\displaystyle\int_{0}^{2\pi }{\int_{0}^{5}{\int_{0}^{12}{dz}\,dr}\,d\theta },$ but if I try to use $\displaystyle \displaystyle\iint_{S}{F\cdot N\,dS},$ I don't get the same result.
How to solve this?