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Math Help - How to integrate (sin x)^2024 + (cos x)^2012

  1. #1
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    How to integrate (sin x)^2024 + (cos x)^2012

    Hi,

    I have problem with integral. How do I itengrate (sin x)^2024 + (cos x)^2012

    thanks,
    Martin
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  2. #2
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    The integral of (sin x)^2024 is done using a reduction formula a million times until you find a pattern.
    Last edited by mr fantastic; May 18th 2010 at 05:00 AM.
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  3. #3
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    weird integral

    The sin(x)^2024 term is only going to be significant when the cos(x)^2012
    term is insignificant, and vice-versa. Therefore I would say you could just
    integrate them separately and add; and obviously the definite integrals of the two terms will be the same over periods of 2*Pi although Pi/2 out of phase.

    The definite integral over 2*Pi of sin(x)^y over x=0..2*Pi seems to settle
    down to a limit L = approx 0.11175 as y increases. (According to Maple;
    unexpected, I would have guessed it would go to 0).

    Therefore a good numerical approximation to your integral from x= 0 to any
    real number s would seem to be 2*(s/2*Pi)*0.11175

    or (0.11175)*s/Pi.

    If the rigor police come around, you haven't seen me.
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