All that remains is to combine all the ingredients to get an approximation to the line integral. This gives us the sum
This is an approximation to the line integral using N segements of the path.
To get the exact value, we should let 
so that we can
pass through every point of C on our way from t = a to t=b. This, as
you can probably guess, leads to an integral:
Notice that the curve C is assumed to be in three dimensions in the above equation, but we could do this in any number of dimensions. However, the path would still be a curve, and therefore only requires one parameter, t, to describe it. Thus, the line integral becomes a one dimensional integral.