If F(z, y) = (Vx + 6y, 3x + Vy) while C consists of the arc of the curve y = 4x - I from (0, 0) to (4, 0) and the line segment from (4, 0) to (0, 0) then: F . di = (Suggestion: Check the orientation of the curve before applying the 2D Curl Theorem.) Add Work Submit QuestionFind the divergence of the vector field F = div F = Add Work Submit QuestionThe curl of the vector field F(x, y, z) = (5z cos(x), 4zsin(x), 7z) is: curl i + j + + k Add Work Submit QuestionThe surface S is the box bounded by the planes a = 3, y = 4, z = 2, and the coordinate planes. If F(x, y, z) = (e sin(y), et cos(y), yz2) then: F . dS = Add Work Submit QuestionThe solid region E lies between the spheres x2 + y + z2 = 4 and a2 + y2 + z2 = 9 in the first octant. Compute the flux of: 1 Z F(x, y, z) = ( 2yet, 9xz, arctan Vaz+ y2 across O E (the boundary of E): flux