A force  F¯=(y2−x2+z2)i^+(3xy−5z)j^+4zk^ is applied on a particle from the point (0,0,0) to the point (2,4,0) in the path shown . If  WA  is the work done by the force in the paths A, then WA =?

The work done by the external force is ∫F→.dS→ . Now here in this case the z coordinate of the motion of the particle is zero. F→=(y2-x2)i^+3xyj^Hence WA=∫02−x2dx+∫043xy dy =[−x33  ]02 +[3y2]04=−83+48=1363