If the integral is [math]\int^{\pi-\epsilon}_{-\pi+\epsilon}d\theta[/math].

 

where [math]\theta[/math] is a angular coordinate.

 

In the riemman integral , i dont understand if tetha follows the path grenn in figure 1, or [math]\theta[/math] follows the path red in figure 2.

I think it'll be the green path. Is [math]\epsilon \geq 0[/math]?

I think it'll be the green path. Is [math]\epsilon \geq 0[/math]?

 

yes, [math]\epsilon[/math] is [math]>0[/math]

Then it'd be the green path, since [math]\theta[/math] has to pass through 0 at some point.

The integration is in the positive direction of theta. That's why it is the green trace.