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Estimate a integral in the complex

  1. Mar 13, 2012 #1
    1. The problem statement, all variables and given/known data

    Let γ denote the portion of the circle lzl = √(ln(3)) which lies in the left-half plane.

    Prove l(∫γ(e^(iz2)/(z-1) dz l ≤ (3pi√(ln(3))/(ln(3)+1)

    Note: the l l around the integral represents modulus.

    2. Relevant equations

    In the past we used this inequality.

    l∫λf(z)/g(z) dz l ≤ max lf(z)/g(z) l * length(lzl)

    3. The attempt at a solution

    So far I found the length of lzl to be 2pi√(ln(3)) and g(z) ≥ √(3) - 1.

    I am not sure about my work on g(z) and for f(z) = le^(iz2) I am very confused as to how to proceed.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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