Piecewise Smooth Curve

A piecewise smooth curve is a curve C that can be broken into finitely many smooth pieces C₁ C₂, ..., C_n where the terminal point of one piece is the initial point of the next (Figure 13.2.9). For example, a curve formed by two or more sides of a rectangle or a polygon is piecewise smooth. The line integral of F(x, y) over a piecewise smooth curve C is defined as the sum

Figure 13.2.9 A Piecewise Smooth Curve from A to B