Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE. ) F (x, y) = (7x6 y + y - 4)i+ (x7 - 4xy - 5) j, y>o f(x, y) = DNEConsider F and C below. F(x, y) = (4 + 2xy2) i+ 2x2yj, C is the arc of the hyperbola y = _ from (1, 1) to X (a) Find a function f such that F = Vf. f ( x, y ) = X (b) Use part (a) to evaluate - F . dr along the given curve C. JcUse Green's theorem to evaluate the line integral along the given positively oriented curve. x2y? dx + y tan"(4y) dy, C is the triangle with vertices (0, 0), (1, 0), and (1, 7) Jc 286043 15 XUse Green's theorem to evaluate F . dr. (Check the orientation of the curve before applying the theorem.) C F(X, y) = x2 + 2, tan (x) ), C is the triangle from (0, 0) to (1, 1) to (0, 1) to (0, 0) tan x + C X