Let $F(x,y,z)=(6x,-2y,5z)$ a vector field and $S$ the surface of the sphere centered at $(1,0,1)$ e radius $5$. Find the flux of $F$ across the surface $S$.
I want to use the Gauss theorem, and my problem is when i use spherical coordinates how can i found the bounds for $\rho$, $\psi$ if the sphere is not centered at the origin.
Thank you
Best Answer
Hint.
Why don't you use integration by substitution using a translation in order to reduce the problem to one where the sphere is centered at the origin?