I want to check my understanding of the line integral: For a scalar line integral, what we have geometrically is the area between a curve a given function, yes? Hence, it can be thought of as a kind of thin wall, correct? And where our function is f(x,y)=1, we have the length of the curve we are integrating over. For a vector line integral, we actually sum of the unit tangent vectors along some curve, right? Thanks in advance.