4.2✶✶ Evaluate the work done P W = = L" F - dr = L" (F, = S" (Fx dx + F, dy) (4.100) by the two-dimensional force F = (x², 2xy) along the three paths joining the origin to the point P = (1, 1) as shown in Figure 4.24(a) and defined as follows: (a) This path goes along the x axis to Q = (1, 0) and then straight up to P. (Divide the integral into two pieces, f = f+f.) (b) On this path y = x², and you can replace the term dy in (4.100) by dy = 2x dx and convert the whole integral into an integral over x. (c) This path is given parametrically as x = t³, y = 12. In this case rewrite x, y, dx, and dy in (4.100) in terms of t and dt, and convert the integral into an integral over t.

4.2✶✶ Evaluate the work done P W = = L" F - dr = L" (F, = S" (Fx dx + F, dy) (4.100) by the two-dimensional force F = (x², 2xy) along the three paths joining the origin to the point P = (1, 1) as shown in Figure 4.24(a) and defined as follows: (a) This path goes along the x axis to Q = (1, 0) and then straight up to P. (Divide the integral into two pieces, f = f+f.) (b) On this path y = x², and you can replace the term dy in (4.100) by dy = 2x dx and convert the whole integral into an integral over x. (c) This path is given parametrically as x = t³, y = 12. In this case rewrite x, y, dx, and dy in (4.100) in terms of t and dt, and convert the integral into an integral over t.