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

Multiple Choice

Use Green's Theorem to find the work done by the force $\mathbf { F } ( x , y ) = \left( 6 x - 7 y ^ { 2 } \right) \mathbf { i } + 3 y \mathbf { j }$ in moving a particle in the positive direction once around the triangle with vertices $( 0,0 )$ , $( 1,0 )$ , and $( 0,1 )$ .

A) 7
B) $\frac { 7 } { 6 }$
C) $\frac { 7 } { 3 }$
D) 42