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Recurrence formula

  1. Apr 21, 2008 #1
    1. The problem statement, all variables and given/known data
    I(subscript n)=integral (from pi/2 to 0) [sin(x)]^n * [cos(x)]^2.

    Show that I (subscript n) = [(n-1)/(n+2)] I(subscript (n-2))

    I think ur meant to use integration by parts on it somewhere but i don't know wat to use it on.
     
  2. jcsd
  3. Apr 21, 2008 #2

    HallsofIvy

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    Since In-2 involves sinn-2[/sub] it seems clear to me that you want to reduce the the power on sinn(x) and you can do that by differentiating (twice). Try an integration by parts (twice) letting u= sinn(x) and dv= cos2(x)dx. (To find v, it might help to remember that cos2(x)= (1/2)(1+ cos(2x))
     
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