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.
The equation for the vector field is: F = < −y, x − 1 > = -y i + (x-1) j
F(r(t)) = (-2sin(t))i + (2cos(t)-1)j
r(t) = 2cos(t)i+2sin(t)j
r'(t) = -2sin(t)i+2cos(t)j
F(r(t))⋅r'(t)= 4sin^2(t)+4cos^2(t)-1
Origin at 315 degrees (315 degrees = 0) and end at 135 degrees (moving counterclockwise). That would mean I start at 0 degrees and end at 180 degrees.
RANGE = 0≤t≤180 or 0≤t≤π.
I just want to check if I've set this problem up correctly or not. Thanks :)