Flux Equations for a Solid Surface and a Curve

[Miike012]

are both of the equations i posted flux equations. one of them is for a surface of a solid and the other is for a curve?

 

[HallsofIvy]

If you meant "Is one of them is for a surface of a solid and the other is for a curve?", yes, the first specifically says "surface" and the second, while you have only given the form, has "ds" rather than "dS" and so is a path integral.

Also, the first is for flux across (through) the surface in 3 dimensions while the second is for flux across the closed path, in 2 dimensions, and so the flow in and out of the region bounded by that closed path.

 

[BruceW]

well the first one is definitely a surface integral because the question says so. The second one is less obvious. The fact that there is only one integral sign might imply that the integral is over a curve...

Is this for a larger homework question? Maybe you can tell which it is meant to be from what the rest of the question says.