Evaluate ∫C < −y, x − 1 > dr where C is the closed piecewise continuous curve formed by the line segment joining the point A(− √ 2, √ 2) to the point B( √ 2, − √ 2) followed by the arch of the circle of radius 2, centered at the origin, from B to A.
2. The attempt at a solution
Vector field, F = < −y, x − 1 > = -y i + (x-1) j
F(r(t)) = (-sin(t))i + (cos(t)-1)j
r(t) = cos(t)i+sin(t)j
r'(t) = -sin(t)i+cos(t)j
Now I need to evaluate that between the regions 0≤t≤π
I just wanted to check if I've set this up correctly. The arc from point B to A is = 180°= π, so that's why I've defined the region of t as going from 0≤t≤π.