Multivariable Calculus (Calc III) - Complete Semester Course - Example using Green's Theorem to compute a circulation integral

In this exercise, we use Green's Theorem for circulation to switch from computing the circulation of a vector field around two closed curves to computing the double integral of the (2D scalar) curl of the vector field over the enclosed region. I emphasize that using the theorem means making the switch--if you are asked to solve this kind of question, you should not do a line integral. However, I forgot to emphasize the importance of making sure the orientation of the boundary is consistent with the statement of Green's Theorem. Otherwise, you may need to switch some signs around! In this case, we didn't need to worry about that because our boundary curves were oriented correctly: if you drive on them, the region R is to your left. Here is my lecture explaining Green's Theorem: https://www.youtube.com/watch?v=ZGOQCs1PymQ #math #mathematics #calculus #multivariablecalculus #lineintegral #greenstheorem #iitjam #iitjammathematics