Need help with practice problem!Therom 3 : |c F dr is independent of path in D if and only if |c F dr = 0 for every closed path C in D

2. Suppose F(x, y) = P(x, y)i + O(x, y)i where P(x, y) and Q(x, y) = x 2 + 1 2 x 2 + 1 2 (a) Find OP and ay Ox (b) Suppose C, is the curve given by: r(1) = (cos(t), sin(t) ) where Out 27 . Find F. dr. (c) Two Calculus three students, Jim and Jenny, are asked to state whether or not F is a conservative vector field on its domain and explain why. Jim makes the following argument: "The vector field F is conservative by theorem 6 on page 1091 of the book Op since _2", Jenny makes the following argument: "Since F . dr # 0 we know by dy Ox theorem 3 on page 1089 of the book that | F . dr is not independent of path. Then, since line integrals of conservative vector fields must be independent of path, we know that F is not conservative". Explain whose argument is incorrect