Advanced Engineering Mathematics, 7th Edition

18.3 Independence of Path

INTRODUCTION

In real calculus when a function f possesses an elementary antiderivative, that is, a function F for which F′(x) = f(x), a definite integral can be evaluated by the Fundamental Theorem of Calculus:

(1)

Note that (x) dx depends only on the numbers a and b at the initial and terminal points of the interval of integration. In contrast, the value of a real-line integral ∫_C P dx + Q dy generally depends on the curve C. However, we saw in Section 9.9 that there exist line integrals whose value depends only on ...