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Math Help - Integrate (Sinx)^2

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    Cool Integrate (Sinx)^2

    Hi!

    How do I integrate (Sinx)^2 ?
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  2. #2
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    Quote Originally Posted by Fredrik373 View Post
    Hi!

    How do I integrate (Sinx)^2 ?
    Recall that \cos^2{x} + \sin^2{x} = 1 and \cos^2{x} - \sin^2{x} = \cos{2x}.

    So if you subtract the second equation from the first...

    (\cos^2{x} + \sin^2{x}) - (\cos^2{x} - \sin^2{x}) = 1 - \cos{2x}

    2\sin^2{x} = 1 - \cos{2x}

    \sin^2{x} = \frac{1}{2} - \frac{1}{2}\cos{2x}.



    Therefore:

    \int{\sin^2{x}\,dx} = \int{\left(\frac{1}{2} - \frac{1}{2}\cos{2x}\right)\,dx}

     = \frac{1}{2}x - \frac{1}{4}\sin{2x} + C.
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