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Math Help - Integration

  1. #1
    Junior Member piglet's Avatar
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    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...
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  2. #2
    MHF Contributor

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    Quote Originally Posted by piglet View Post
    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!
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