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Math Help - sin integral

  1. #1
    s7b
    s7b is offline
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    sin integral

    Quick integral

    How to you take the integral of sin^4(x)
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  2. #2
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    sin(x)^4 = [(1 - cos(2x)) / 2]^2 // half-angle identity
    1/4 - cos(2x)/2 + cos(2x)^2/4 // expand
    1/4 - cos(2x)/2 + 1/4((1 + cos(2x)) / 2) // half-angle identity
    3/8 - cos(2x)/2 + cos(2x)/8 // simplify
    3/8x - sin(2x)/4 + sin(2x)/16 // integrate

    Hoping I didn't get lost along the way. =p Still don't know how to use the math notation.

    Edit: Whoop, sorry, second half-angle identity should have been (1 + cos(4x)) / 2. Answer's the same, but the last term is sin(4x)/32
    Last edited by derfleurer; April 19th 2009 at 02:56 PM.
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