all circles positively oriented. Use Cauchy's Integration Formulas to compute each of the following integrals. HINT: use partial fractions where appropriate.
a)
b)
c) , t>0
The Cauchy integral formula :
NOW FOR c) in the denominator -1 is interior to C so i go as follows,
so n=2 in the extension of Cauchy's integral formula given as
so i let f(z) = then f'(z) = and f ''(z) =
hence f '' (-1) = and then by the extended Cauchy integral formula i get
, is this correct ?
OK, things i don't know :
Now in a) neither 3 nor -1 are interior to C so neither of them are my Zo point. The same goes for b) in the denominator neither 0 nor 1 are interior to C, so where do i find Zo ? Now if the answer is to use partial fraction decomposition, my attempt :
for a)
and now what ? How do i equate anything??? I have the same confusion for b). I aprreciate any help.