Topic: Line integrals (Green's Theorem and conservative vector fields)

There are four questions below. Show all your works!!!

1. Find the Divergence and Curl of the given vector filed. Q: F = Vf, where f(x, y) = xy. In Exercises 7 - 12, a vector field F and a curve C are given. Evaluate / F . dr. 8. F = (x, x + y); C is the portion of the parabola y = x from (0, 0) to (1, 1). 12. F = (y + z, x + z, x + y); C is the helix F(t) = (cost, sint, t/(27)) on 0 S t S 2n. In Exercises 5 - 10, a planar curve C is given along with a surface f that is defined over C. Evaluate the line integral / f(s ) as. 7. Cis the circle with radius 2 centered at the point (4, 2); the surface is f(x, y) = 3x - y