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Math Help - integrate sin^4(x)

  1. #1
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    integrate sin^4(x)

    hey guys im trying to integrate sin^4(x) can someone check over this and tell me if its correct:


    = sin(4x)/32 - sin(2x)/4 + 3x/8

    is that the correct answer for the integration of sin^4(x)
    Last edited by quickzxxx; May 15th 2009 at 02:57 AM. Reason: pics didnt work
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  2. #2
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    Hello,
    Quote Originally Posted by quickzxxx View Post
    hey guys im trying to integrate sin^4(x) can someone check over this and tell me if its correct:

    = sin(4x)/32 - sin(2x)/4 + 3x/8

    is that the correct answer for the integration of sin^4(x)
    your answer is correct (don't forget the integration constant !)
    Last edited by mr fantastic; May 15th 2009 at 04:04 AM.
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  3. #3
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    You don't have to use de Moivre's formula to solve this.

    \sin^4 x = \frac{1-\cos 2x}{2}\cdot \frac{1-\cos 2x}{2}=\frac{1}{4}(1-2\cos 2x + \cos^2 2x)= \frac{1}{4}\left(1-2\cos 2x + \frac{1}{2}(1+\cos 4x)\right)=\frac{1}{8}\cos 4x - \frac{1}{2} \cos 2x + \frac{3}{8}
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