December 2020
Intermediate to advanced
1064 pages
49h 43m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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9.8 Line Integrals
INTRODUCTION
The notion of the definite integral 
; that is, integration of a function defined over an interval, can be generalized to integration of a function defined along a curve. To this end we need to introduce some terminology about curves.
Terminology
Suppose C is a curve parameterized by x = f(t), y = g(t), a ≤ t ≤ b, and A and B are the points (f(a), g(a)) and (f(b), g(b)), respectively. We say that
(i) C is a smooth curve if f′ and g′ are continuous on the closed interval [a, b] and not simultaneously zero on the ...