14. F(x, y) = 3xe-i, c consists of line from (2, 4) back to (0, 0) 15. F(x, y) = 2xi/(x² + y) +j/(x² + y), c is the boundary of the rectangle [1, 2] x [0, 1], oriented counterclockwise 16. F(x, y) = x sin yi + y sin xj, c is the boundary of the triangle defined by the lines y=x, y= y = x/2, and x = 1, oriented counterclockwise 17. F(x, y, z) = yi +2zj + 3xk, c is the intersection of the cylinder x² + y² z = y, oriented counterclockwise as seen from above = 1 and the plane 18. F(x, y) = (2xyi + j)e", c consists of the straight-line segments from (0, 0) to (1, 1), then from (1, 1) to (0, 2), and then from (0, 2) back to (0, 0) 19. F(x, y, z) = xi-yzj+k, c is the intersection of the paraboloid z = z = 2y, oriented counterclockwise as seen from above x²+ y² and the plane 20. F(x, y, z) = 5i + 2j+ zk, c is the ellipse y²+4z2 = 4 in the plane x = 2, oriented clockwise as seen from the origin 21. F(x, y, z) = (2x+y)i + (2y-x)j, c is the helix c(t) = (cost, sint, t), t = [0,3], followed by the line segment from (-1, 0, 3л) back to (1, 0, 0) 22. Show that if the curve c = aS and the surface S satisfy the assumptions of Stokes' Theorem, then ffVg ds = fs (Vfx Vg) dS. 23. Show that if the curve c = aS and the surface S satisfy the assumptions of Stokes' Theorem, hen ffVf ds = 0 4. Set up the integral for the counterclockwise circulation of the vector field F = ei/(x²+1) ound the unit circle in the xy-plane. Then evaluate it using Stokes' Theorem. IAL FORMS AND CLASSICAL INTEGRATION THEOREMS