Calculate the Work Done by the Force Field When a Particle Moves Under Its Influence Around the Edge

Short Answer

Calculate the work done by the force field $\mathbf { F } ( x , y , z ) = \left( x ^ { 2 } + 10 z ^ { 2 } \right) \mathbf { i } + \left( y ^ { 2 } + 14 x ^ { 2 } \right) \mathbf { j } + \left( z ^ { 2 } + 12 y ^ { 2 } \right) \mathbf { k }$ when a particle moves under its influence around the edge of the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ that lies in the first octant, in a counterclockwise direction as viewed from above.