Chapter 48-49 Anti-derivatives

Question 1

Thm pg 141 w/ preamble conditions (3equiv for antiderivs)

Answer 1

f cont on domain D

1. f has an antideriv on D
2. line integral of f is indep of path in D
3. if C is a closed contour in D, then
   $\int_c f(z) dz = 0$

Question 2

Cauchy-Goursat theorem

Answer 2

If f is analytic at 
1) all pts interior t and
2)on
a simple closed curve C, then
$\int_c f(z) dz = 0$