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**1. Homework Statement**

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)

r

**i**+sin(t)

**j**

r'(t) = -sin(t)

r

**i**+cos(t)

**j**

F(

F

**r**(t))

**⋅r**'(t)=sin

^{2}(t)+cos

^{2}(t)-1

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.