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Math Help - Integral Help - integral of (cos^6)(x)

  1. #1
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    Integral Help - integral of (cos^6)(x)

    What is the integral cos6(x)? I just want to make sure I am correct.
    The answer I got was [(3sin(4x) + 2sin(2x) + 5x)/16] + C
    but I have no clue if I am correct and am not very confident in my integration skills.
    If your answer is different, it'd be a great help if you could show me the process you took to get there.

    Thanks!
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  2. #2
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    Re: Integral Help - integral of (cos^6)(x)

    No that's not correct try using the reduction formula.
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  3. #3
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    Re: Integral Help - integral of (cos^6)(x)

    hint:
    \int cos^{m}(x)dx=\frac{sin(x)cos^{m-1}(x)}{m}+\frac{m-1}{m}\int cos^{m-2}(x)dx
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  4. #4
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    Re: Integral Help - integral of (cos^6)(x)

    No I don't think it is correct because the derivative of [(3sin(4x) + 2sin(2x) + 5x)/16] + C
    is not equal to cos6(x) . Moreover you didn't show to us how you did it...
    Anyway use repeated integration by parts and you will get it...but be patient because the process is lengthy...


    Good Luck
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  5. #5
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    Re: Integral Help - integral of (cos^6)(x)

    SMAD - I don't think the reduction formula is within the scope of my course, so if this question comes up in my exam I don't think I will get marks for process.
    Do you know of another way to do it?

    MINOANIMAN- Yeah, I thought so, My working took more than a page (possibly because of my relatively large handwriting) so I didn't post that sorry, but I broke up the cos^6(x) into (cos^2(x))^3 and substituted the half angle formula (cos^2(x) = 1/2(1+cos(2x)) and went from there, but I may have made some algebraic errors that I can't see... :\ I'm just wondering if there's a better way to break it up that will result in less possible errors.

    Thanks for your help!
    Last edited by toga; October 19th 2013 at 05:05 AM.
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  6. #6
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    Re: Integral Help - integral of (cos^6)(x)

    No you have to do as I said by repeated integration by parts without breaking into cos2x ....just follow the formula...I said it is lengthy

    the correct answer is :

    Integral Help - integral of (cos^6)(x)-integral.png
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