A force acting on a particle moving in the xy plane is given by F = ( 2yi + x^2 j ), where F is in newtons and x and y are in meters. The particle moves from the origin to a final position having coordinates x = m and y = m as shown in Figure P7.43. Calculate the work done by F on the particle as it moves along (a) the purple path, (b) the red path, and (c) the blue path. (d) Is F conservative or nonconservative? (e) Explain your answer to part (d).