I'm learning surface integrals right now and I don't think I fully understand what they are. What exactly do surface integrals represent? Is it volume? The basis for surface integrals seems just like a standard double integral using some surface.
Like any integral it is adding up a continuous thing over an area. In context this can mean a variety of different concepts. It could be a volume if the function is representing height - this is probably a good analogy to start with - but it could be far harder to conceptualize depending on the situation.
In fluid dynamics if we had different pressures over the surface of an object then the integral of the pressure over that area would give the total force pushing on the object.
In optics if we shone a light on a wall then the integral of the intensity of the light over the surface area of the wall would relate to the energy produced by the light.