Guys, so Gauss’ theorem states that
$$
\int_V\nabla\cdot F\,dV=\int_S F\cdot\,dA.
$$
I have to verify the divergence theorem in the case where the surface is a spare of radius $R$ centered at the origin, and $F=(x,y,z)$.
Apparently the solution is $1+1+1=3$. How did they come up with that? Did they do something like this: $\int_V\frac{\partial F_x}{\partial x}dV=1$?
$$
\int_V\nabla\cdot F\,dV=\int_S F\cdot\,dA.
$$
I have to verify the divergence theorem in the case where the surface is a spare of radius $R$ centered at the origin, and $F=(x,y,z)$.
Apparently the solution is $1+1+1=3$. How did they come up with that? Did they do something like this: $\int_V\frac{\partial F_x}{\partial x}dV=1$?
