So, in answering this question the book resolves the components of the Force vector in this manner;
- $\mathrm dF_x= \mathrm dF \sin \theta$
- $\mathrm dF_y= \mathrm dF \cos \theta$.
And then, it integrates from $\theta_0$ to $2\pi-\theta_0$.
I don't understand why are the x and y components reversed and not depending on cos and sin respectively.
I also don't understand why are the limits of integration in this manner, since I thought this way the part of the circle that we are going to be leaving out is the right corner of the circle instead of the top.