1. The problem statement, all variables and given/known data *Questions 3, 5 and 6 have already been answered. 1) On page 1091, am I right to assume that example 4 could be solved using Green's Theorem? 2) How about for example 6, on page 1093, or would we need a higher dimensional analog? 3) What is the meaning of ""ds" in example 1 of page 1064? How is ds related to dx and dy? Intuitively, what is the difference between example 1 and example 4? 4) Does the Fundamental Theorem for Line Integrals only work for vector fields? If so, should I automatically use the Fund Thm of Line Integrals for vector fields? 5) The only difference between a line integral and a vector field is the use of ##\vec i## and ##\vec j## in place of dx and dy. Is ##\int_C F \cdot dr ## a line integral, or is it a vector? If it's a vector, is it a field or a function? 6) When solving a line integral, how do I know when to use Green's Thm, the Fund Thm of Lne int, or the classic method of using parameters? Would I be told what to do on the exam? 7) On page 1082, question 15 is conservative. Solving using the Fund Thm of Line Int gives 77. Using Green's theorem, the answer is zero. Why is there a difference? 8) Why is example 4 of page 1112 "not simple" while exercise 10 of page ##1090## is? 9) What is the difference between "closed" "simple" and "conservative"? 2. Pictures of my textbook Attached Click to enlarge the above: 1091, 1093, 1112, 1114 3. The attempt at a solution Thank you.