Question

1. Let D be the plane region bounded by the upper-half of the circle with equation
( x−1)2+ y2=4 and the x-axis. Furthermore, let F (x , y)=< x2−3 x y , 2 x > be a vector field.
a) Determine the value of ∮∂ D F⋅ds by direct computation.
b) Verify your answer using Green's Theorem.