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Math Help - Integral problem

  1. #1
    Junior Member
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    Integral problem

    Given: \int_0^{2\pi} \cos^2{6\theta} \, d\theta
    _____________________________________________

    Attempt: \int_0^{2\pi} \cos^2{6\theta} \, d\theta = \int_0^{2\pi}\ \frac{1-sin^2{12\theta}}{2}\, d\theta = \int_0^{2\pi}\ \frac{1}{2}\, d\theta -\frac{1}{2}\int_0^{2\pi} 2sin{6\theta}\, cos{6\theta}\, d\theta = \frac{1}{2}( 2\pi - 2) = \pi - 1

    The answer is supposed to be just \pi. Can I get any help here? Thanks.
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    Try instead

     <br />
\int \cos^2(6\theta) ~d\theta = \int \frac{\cos (12\theta)-1}{2} ~d\theta<br />
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