"What's the magnitude that's going in the normal direction?" so essentially, what's the magnitude of that vector right over there it's going to be in kilograms per meter second and we're multiplying it times ds we're multiplying it times this infinitesimally small segment of the curve we're going to multiply that times ds well, what are the units of ds? it's going to be unit of length we'll just go with meters so this right over here is going to be meters there's this whole integral, you're going to have kilogram per meter second times meters so if you have kilograms per meter second and you were to multiply that times meters, what do you get? well this meters is going to cancel out that meters and then you get something that kinda starts to make sense you have kilogram per second and so this hopefully this makes it clear what's going on here this is telling us how much mass is crossing that little ds that little section of the curve per second and if you were to add up- and that's what integrals are all about, adding up an infinite number of these infinitesimally small ds's if you add all of that up you're going to get- the value of this entire integral is going to be in kilograms and kilograms per second, and it's essentially going to say,