# Integration

• Mar 6th 2010, 02:40 AM
piglet
Integration
Just looking for a bit of guidance or perhaps just clarification...

I have to integrate f(z) counterclockwise around the unit circle where

f(z) = 1/(z^4 + 1.1)

My first attempt at solving this was to sub in e^it for z. Then I let u = e^it
which left me with the integral of: du/(u^4 + 1.1). I, then proceed to integrate the function and subbed back in e^it for u after i had integrated. Finally I evaluated the result of my integral between 0 and 2pi, to which i got an answer of 0

Question
: Is this a valid way of trying to solve a problem like this?

p.s. I tryed another method in solving this problem. This involved letting the denominator of f(z) = 0 to find the pts. at which f(z) was not analytic. I found that as these pts. lay outside the unit circle that i could use cauchy's integral theorem to state that the integral of f(z) is 0...

Again im not sure if this a valid method...
• Mar 6th 2010, 03:52 AM
HallsofIvy
Quote:

Originally Posted by piglet
Just looking for a bit of guidance or perhaps just clarification...

I have to integrate f(z) counterclockwise around the unit circle where

f(z) = 1/(z^4 + 1.1)

My first attempt at solving this was to sub in e^it for z. Then I let u = e^it
which left me with the integral of: du/(u^4 + 1.1). I, then proceed to integrate the function and subbed back in e^it for u after i had integrated. Finally I evaluated the result of my integral between 0 and 2pi, to which i got an answer of 0

Question
: Is this a valid way of trying to solve a problem like this?

p.s. I tryed another method in solving this problem. This involved letting the denominator of f(z) = 0 to find the pts. at which f(z) was not analytic. I found that as these pts. lay outside the unit circle that i could use cauchy's integral theorem to state that the integral of f(z) is 0...

Again im not sure if this a valid method...

Yes, both of those are valid methods- the second being easier, of course!