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Findinf residue of 1/5+4sin(deta)

  1. Dec 11, 2012 #1
    1. The problem statement, all variables and given/known data
    it ask me to integral from 0 to 2pi for 1/[5+4sin(deta)]


    2. Relevant equations
    i knoe i nid to find out the pole bu convert sin(deta) into exponential fomat

    3. The attempt at a solution
    after i solve it until 2z^2+5iz-2 i stucked,can i juz use [-b+-squarot[b^2-4ac]]/2a formula to solve this by juz let my b=5i?
    and i get the answer is in negative value,if i do that.i think i might wrong ,any one can help me?
     
  2. jcsd
  3. Dec 11, 2012 #2

    Dick

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    Yes. You can use the quadratic equation to solve something like that. But I don't think you've got the right quadratic and I don't know what "i get the answer is in negative value". You really need to show your work.
     
  4. Dec 11, 2012 #3
    ∫1/5+4sin(deta) dθ =∫(dz/iz)/[5+4(z/2i-1/2iz)]
    = ∫(dz)/[5iz+4(iz^2/2i-iz/2iz)]
    = ∫(dz)/[5iz+(4iz^2)/(2i)-4iz/2iz)]
    =∫(dz)/[5iz+2z^2-2]

    then i nid solve 5iz+2z^2-2 to get my pole,am i wrong??? then i will get my root in -0.5i and -2i.
     
  5. Dec 11, 2012 #4

    Dick

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    Yep, that's what I get. I made a mistake but I caught it thanks you to showing what you did.
     
    Last edited: Dec 12, 2012
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