Use Green's Theorem to evaluate the line integral along the given positively oriented curve. (5y + 9evx) dx + (10x + 7 cos(y2)) dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2 EXAMPLE 3 Determine whether or not the vector field F(x, y) = (2 + 8xy)i + (4x2 – 6y2); is conservative. SOLUTION Let P(x, y) = 2 + 8xy and Q(x, y) = 4x2 – 6y2. Then ad aQ - ду Also, the domain of F is the entire plane (D = R2), which is open and simply-connected. Therefore we can apply this theorem and conclude that
