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Definite integration problem

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  1. Jan 31, 2015 #1
    1. The problem statement, all variables and given/known data
    ∫dt/(t^2 +2tcos a + 1)
    (Limits of the integral are from 0 to 1)
    (0<a<π)
    2. Relevant equations


    3. The attempt at a solution
    Put t=sin a
    dt=cosa da
    ∫dt/(t^2 +2tcos a + 1) = ∫cos a da/(sin^2 a + sin 2a + 1) [ limits of integration changed to 0 to π/2]
    = ((cosec a)/2) ∫sin 2a da/(sin^2 a + sin 2a + 1)

    I couldn't figure out what to do next... Please help!!
     
    Last edited by a moderator: Jan 31, 2015
  2. jcsd
  3. Jan 31, 2015 #2

    Mark44

    Staff: Mentor

    I don't know what you did in this last step, but you can't bring csc(a) out as if it were a constant.
     
  4. Jan 31, 2015 #3
    Oh yes... By mistake i typed the integration symbol after it. Cosec a should be inside the integral. So, how should i proceed??
     
  5. Jan 31, 2015 #4

    Mark44

    Staff: Mentor

    I would try a different substitution -- let t = cos(a).That should get you an integral that's easier to do.
     
  6. Jan 31, 2015 #5
    Oh yah... Thanks ... I solved it... But have a look at this file... I couldn't get an answer for this... New Doc 1_1.jpg
     
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