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Math Help - problem in integration

  1. #1
    Junior Member
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    problem in integration

    I'm supposed to integrate
    pi
    ∫ (cos nx)(cosx)^2 dx
    0

    how do i integrate this?
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  2. #2
    MHF Contributor
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    My first guess would be convert \cos^2(x) to 1-\sin^2(x) and then it becomes a trivial integral plus a u-sub one.
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  3. #3
    Super Member
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    First, use the half angle identity to get rid of the cos^2(x).

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

    Multiplying this with \cos{nx} will get you

    \frac{1}{2} \int (\cos{nx} + \cos{nx}\cos{2x}) dx

    First one should be easy. For the second one, you can use either integration by parts or the product to sum identity:

    \cos{a}\cos{b} = \frac{1}{2}(\cos{(a-b)}+\cos{(a+b)})
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  4. #4
    MHF Contributor
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    I didn't see the (nx) term. Sorry. Obviously the above substitution is the one to go with now.
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