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
$$\mathbf { F } ( x , y ) = \left( 4 x - 9 y ^ { 2 } \right) \mathbf { i } + 6 y \mathbf { j }$$
in moving a particle in the positive direction once around the triangle with vertices $( 0,0 ) , ( 1,0 )$ , and $( 0,1 )$ .