Integral over a barrel

In this video, I present a challenging vector calculus problem involving Stokes' theorem: Namely, calculate the surface integral of curl(F) over a barrel as in the thumbnail. What makes this hard is that you have to choose the orientation of your boundary curves to match the orientation of the surface, and the right-hand-rule completely fails for that one. I also illustrate how to calculate line integrals where the orientation is reversed. Enjoy!

Видео Integral over a barrel канала Dr Peyam