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Integration by parts

  1. May 4, 2014 #1
    1. The problem statement, all variables and given/known data
    attachment.php?attachmentid=69417&stc=1&d=1399253516.png


    2. Relevant equations

    N/A

    3. The attempt at a solution

    I cant even begin the attempt because I dont know how you could use intergration by parts for this sum in the first place.
    Can you help me out?
     

    Attached Files:

  2. jcsd
  3. May 4, 2014 #2

    SteamKing

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    First of all, I(n) is not a sum. I is a function which depends on the exponent of the sine function in the integrand.

    You might try to determine what I(n) is for some discrete values of n, like n = 2, 3, 4, etc. and see if a pattern emerges.
     
  4. May 4, 2014 #3

    SammyS

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    What sum ?

    Let u = sin(n-1)(x), and dv = sin(x) dx

    (The King beat me by fractions of a minute!)
     
  5. May 4, 2014 #4

    lurflurf

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    hint
    $$\int\! \sin^n(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\sin^{2}(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\big(1-\cos^{2}(x)\big) \, \mathrm{d}x$$
     
  6. May 4, 2014 #5
    This does not look like precalculus.
     
  7. May 4, 2014 #6
    Lol. He did.

    Anyways, can you tell me why sin(n-1)(x)?
     
  8. May 4, 2014 #7

    SammyS

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    (n-1) is half way from n to (n-2) .


    Try it and see what happens !
     
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