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Math Help - Trig integrals

  1. #1
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    Trig integrals

    Can someone just explain to me how these integrals work? I don't remember the identities well enough to do these haha..



    integral of cos^2(2theta)
    integral of sin^2(4theta)
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  2. #2
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    Quote Originally Posted by coolguy99 View Post
    Can someone just explain to me how these integrals work? I don't remember the identities well enough to do these haha..



    integral of cos^2(2theta)
    integral of sin^2(4theta)
    Use the double angle formulae:

    cos(2A) = 2cos^2(A) - 1 ---> cos^2(A) = \frac{cos(2A) + 1}{2}

    In this case A = 2\theta

    cos(2A) = 1-2sin^2(A) -------> \frac{1-cos(2A)}{2}

    In this case A = 4\theta

    ------------

    Also \int sin(Ax)dx = -\frac{1}{A}cos(Ax) + C

    \int cos(Ax)dx = \frac{1}{A}sin(Ax) + C
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