# Math Help - Trigometric for odd function

1. ## 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 ?

2. Originally Posted by Chris0724
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 $f(x) = (1-x^2)^n$