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Definite integral question

  1. May 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the value of ∫ ( sin 37x / sin x )dx - from 0 to π


    2. Relevant equations



    3. The attempt at a solution
    Well i tried doing it by parts but it makes its more complicated. I tried to expand sin 37x as sin(36+1)x but could not solve it. I am lost
     
  2. jcsd
  3. May 7, 2012 #2

    Ray Vickson

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    [tex]\sin(nx) = \frac{1}{2i} ( X^n - Y^n), \text{ where } X = e^{ix}, \: Y = 1/X. [/tex]
    Thus, [itex] \sin(nx) = \sin(x) [X^{n-1} + X^{n-2}Y + \cdots + Y^{n-1}], [/itex] so
    [tex] \sin(nx)/\sin(x) = X^{n-1} + X^{n-2}Y + \cdots + Y^{n-1}. [/tex]

    RGV
     
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