1 (4.4.4 ) Although it is not defined on all of space R", the field associated with the line integral below is simply connected, and the component test can be used to show it is conservative. Find a potential function for the field and evaluate the integral. A general expression for the infinitely many potential functions is f(x.y.z) =]. 2 (9.9. - 2) Evaluate the integral y dx + x dy + 2 dz by finding parametric equations for the line segment from (4,3,3) to (9.9. - 2) and evaluating the line integral of F = yi + xj + 2k along the segment. Since F is conservative, the integral is (4,3,3) independent of the path. (9.9. - 2) y dx +x dy+ 2 dz= (4.3,3 3 Find the work done by F = (x2 + y) I+ (2 +x)] +zeck over the following paths from (2,0,0) to (2,0,4). 2,0,4) a. The line segment x = 2, y = 0, 0szs4 b. The helix r(t) = (2cos t)i + (2sin t)j + - k, Osts2x (0,0,0) c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola (2,0,0) z=x, y=0 from (0,0,0) to (2,0,4) a. Find a scalar potential function f for F, such that F = Vf. O A. 2 x 3 + x 2 y2 + my3 + ez + c O B . 2 x 3 + xy + my 3 + ze