Can someone explain what is the purpose of surface integrals? How are they different from flux integrals?
Edit: the explanations already on this sub did not help that much sorry
In: Mathematics
Flux is to find the flow of a vector field through a surface. Specifically you will see the dot product of vector F and dS vector. A surface integral doesn’t necessarily have to calculate flux. It could calculate the surface area instead or the total force on a scrap of metal in space due to gravity.
Below I use F as a general vector field, it doesn’t necessarily represent force.
Below is latex
Flux
$oiint_{S}{vec{F}cdotvec{dS}}$
Surface area
$oiint_{S}{dS}$
General Surface Integral
$oiint_{S}{vec{F} dS}$
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