Suppose we have a vector field $\mathbf{E}$ and a surface $S$. What is the formula for the average of $\mathbf{E}$ over the surface?
My attempt:
I think it is $\displaystyle\frac{1}{\text{area(S)}}\oint_S\mathbf{E}da$ where $da$ is the infinitesimal area element, but I could be mistaken.