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Math Help - Need Help with Trig Integration

  1. #1
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    Need Help with Trig Integration

    As part of a larger problem I came across 1/8 the integral of cos^3(2x).
    I simplified this to 1/16 the integral of 2(1-sin^2(2x))cosx and then solved with u substitution.
    u=sin(2x)
    du=2cos(2x)

    This came out to [sin^3(2x)]/48.
    My teacher tells me that the answer is [sin^3(2x)]/6. I don't see how this is possible. Who is right?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    I disagree with your teacher and you--though I agree with you in part

    Note if you differentiate your result you get part of the answer but not all

    See attachment
    Attached Thumbnails Attached Thumbnails Need Help with Trig Integration-integral.jpg  
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