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Integration by parts

  1. Jun 12, 2009 #1
    1. The problem statement, all variables and given/known data

    latex2png.2.php?z=200&eq=%5Cint_%7B0%7D%5E%7Bpi%2F6%7Dcos%5E2(2x)dx.jpg
    1. The problem statement, all variables and given/known data

    3. The attempt at a solution
    u= cos(2x) = > du= -2 sin(2x)
    dv=cosx(2x) =>v= 1/2 sin(2x)
    ?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 12, 2009 #2

    HallsofIvy

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    And the formula for integration by parts is
    [tex] uv- \int v du[/tex]
    which, here, is
    [tex](1/2)sin(2x)cos(2x)+ \int sin^2(2x)dx[/tex]

    Not really an improvement is it? Are you required to use integration by parts? I would use the trig identity [itex]cos^2(u)= (1/2)(1+ cos(2u))[/itex].

     
  4. Jun 12, 2009 #3
    The above identity is probably the easiest way to go, but if you're determined to use integration by parts, try integrating the
    [tex] \int_0^{\frac{\pi}{6}} \sin^2(2x) [/tex]
    and see where you end up.
     
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