Suppose I am calculating the (homogenous) electric flux through a straight line. How do I calculate the surface integral of a straight line? Is it simply a line integral, or is it more complex (I don't think the first is true because if the surface integral is a measure of area, but the line integral is a measure of length). I found this on wikipedia.
In mathematics, a surface integral is a definite integral taken over a surface. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return scalars as values), and vector fields (that is, functions which return vectors as values).
Basically, how do I calculate the surface integral of a line y= mx+c? What about more complex curves, for example the Archimedean Spiral ($r= a+ b \theta$ in polar form)?