Complex variables

Complex variables

a Show that the definition of a complex line integral along a piecewise C curvey on [a, b] is independent of the partition of [a, b] used (see Definition 2.6.2) in your textbook) Suggestion: The idea is easy but a bit technical. Let P and P2 be two partitions of (a, b) such that y is Cl on the subintervals induced by each of these partitions. Suppose that their symmetric difference, Pi AP2, contains only one point, say a*. Without loss of generality, you may assume that P2 = P1 U{a*} and that Ak-1