Thanks in advance

1) Let f (x, y) = 4x cos (y). Find the conservative vector field F, which is the gradient of f. Evaluate the line integral of F over the upper half of the unit circle centered at the origin, oriented clockwise. 2) Let F (x, y) = , . Calculate the work against F required to move an object from (1, 1) to (4, 5) along any path in the first quadrant.3) A vector field F and contour lines of a potential function for F are shown in the figure. 25 19 13 X Calculate the common value of F dr for the curves in the direction from P to