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Math Help - Trigometric for odd function

  1. #1
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    Trigometric for odd function

    For trigometric if the integrand inside the integral (i.e., the function to be integrated in theta )is ODD.

    How do we approach the problem? is there a way ?
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  2. #2
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    Quote Originally Posted by Chris0724 View Post
    For trigometric if the integrand inside the integral (i.e., the function to be integrated in theta )is ODD.

    How do we approach the problem? is there a way ?

    If the function can be transformed to this form :

     g(\theta) = \sin(a\theta)f(\cos(a\theta))

    For finding the anti-derivative , we just sub.

     x = \cos(a\theta)  ,~~  \sin(a\theta) ~ d\theta = -\frac{1}{a}dx

     I = -\frac{1}{a} \int f(x) ~dx


    We can always find out such function but hardly transform it to that form ( not impossible )


    For example ,

     g(\theta) = \sin^{2n+1}(\theta)

    we have  f(\cos(\theta)) = \sin^{2n}(\theta)

    so  f(x) = (1-x^2)^n
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