Advanced Engineering Mathematics, 7th Edition

9.9 Independence of Path

INTRODUCTION

In this section we refer to a piecewise-smooth curve C between an initial point A and a terminal point B as a path of integration or simply a path. We begin the discussion by considering line integrals in 2-space. Recall, in (10) of Section 9.8 we saw that if F(x, y) = P(x, y)i + Q(x, y)j is a vector field in 2-space and a path C is defined by the vector function then a line integral can be written as

where dr = dxi + dyj. Generally the value of a line integral depends on the path of integration. Stated ...