Use Green's Theorem to Find the Work Done by the Force

Short Answer

Use Green's Theorem to find the work done by the force
$$\mathbf { F } ( x , y ) = x ( x + 3 y ) \mathbf { i } + 3 x y ^ { 2 } \mathbf { j }$$
in moving a particle from the origin along the $x$ -axis to $( 1,0 )$ then along the line segment to $( 0,1 )$ and then back to the origin along the $y$ -axis.