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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- Nov 28th 2009, 08:39 PMChris0724Trigometric 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 ? - Nov 28th 2009, 10:02 PMsimplependulum

If the function can be transformed to this form :

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

For finding the anti-derivative , we just sub.

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

$\displaystyle 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 ,

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

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

so $\displaystyle f(x) = (1-x^2)^n $