1. (3pts) Suppose the curve C consists of the line segment connecting (0,0,0) and (1,0,0) and the line segment connecting (1,0,0) and (1,1,1). Use the Fundamental Theorem of Line Integrals to find the exact value of: | y dx + x dy + z dz .\f(c) (2pts) Two Calculus III 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 the last theorem on page 7 of the 5.3 notes since ap co "> Jenny makes the following ay Ox argument: "Since F. dr #0 we know by the last theorem on page 4 of the 5.3 notes that | F. dr is not C 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. Extra Credit (2pts): show all w