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Integration by parts, just need a small hand

  1. May 20, 2015 #1
    1. The problem statement, all variables and given/known data
    I'm going to cut from the initial part of the problem, which I am confident is good to go, and cut straight to the antiderivatives.

    2. Relevant equations
    All antiderivatives are to be integrated on the interval from 0 to π/18

    (I1) = -1/9 cos 9x - (I2) (-2/27 * cos3(9x)) + (I3) (-1/45 * cos5(9x)

    3. The attempt at a solution
    For I1 -- (π)/18) -- -1/9 cos 9π/18 = -1/9 cos π/2 = 0
    -1/9 cos 0 = -1/9
    0 - (-1/9) = 1/9

    ForI2 -- ( π/18) -- -2/27 cos 9π/18 = -2/27 cos π/2 = 0
    -2/27 cos 0 = -2/27
    0 - (-2/27) = 2/27

    For I3 -- (π/18) -- -1/45 cos 9π/18 = -1/45 cos π/2 = 0
    -1/45 cos 0 = -1/45
    0- (-1/45) = 1/45

    1/9 - 2/27 + 1/45 = 8/27, or 40/135 -- However, the answer in my text is 8/135.

    Again, I am positive on my getting the antiderivatives right, I am sure the error is in the computing of the definite integrals. I thank you in advance for all help.

    SY
     
    Last edited: May 20, 2015
  2. jcsd
  3. May 20, 2015 #2

    Ray Vickson

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    Your individual terms are correct and your almost-answer of ##1/9 - 2/27 + 1/45## is correct, but your arithmetic is wrong after that.
     
  4. May 20, 2015 #3
    Got it, thank you very much for your help -- (15 - 10 + 3) / 135 = 8/ 135 -- just needed a push in the right direction.
     
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