I appreciate any feedback for my question.
I have an integration as follows
$$\int_{-\pi}^{\pi}\frac{1}{2\pi} \prod_i \frac{1}{1+ x_ig(\theta)} d\theta $$
I have that $g(\theta)$ is the defined as piecewise
$$ g(\theta) = \left\{ \begin{array}{ll} 1 & \mbox{if $\theta_{min} \leq \theta\leq \theta_{max}$};\\ 0 & \mbox{if $OW$}.\end{array} \right. $$
Can I do the following to solve my integration? $$\int_{\theta_{min}}^{\theta_{max}}\frac{1}{2\pi} \prod_i \frac{1}{1+ x_i 1} d\theta $$ $$=\frac{(\theta_{max}-\theta_{min})}{2\pi} \prod_i \frac{1}{1+ x_i 1} $$
Cheers!