As we have seen, parametrizing surfaces and determining the orientation induced by a parametrization can be quite complicated. Which aspects of parametric surfaces/orientation of surfaces did you find most challenging? What did you do to address these challenges? We have also seen that the process of calculating surface integrals (scalar and flux) is often a long process with several steps. For you, what has been the most challenging part about our study of surface integrals? What have you done to address these challenges? Now that we have seen Stokes' Theorem, we have seen all of the theorems/strategies in this course that help us calculate vector line integrals (for vector fields on R? and R). Which strategy is your favourite? Which is your least favourite? Are there any that you will need to review more than others before the final exam? Suppose you have a surface parametrized by r(u, v). In plain language (without mathe- matical notation), explain the geometric significance of the vectors Or dr Or and Or du' dv In plain language (without mathematical notation), briefly explain what is meant by an orientation of a surface. If S is an oriented surface with boundary curve C, how do you determine the positive orientation of C? In plain language (without mathematical notation), explain how Stokes' Theorem can help you calculate a line integral of a vector field on R3. Suppose F is a vector field on R and you are asked to calculate a line integral F. dr, but it seems too complicated to calculate directly. In a couple of sentences, explain what options you have for strategies to calculate the line integral, and how you would go about determining which strategy to use.