Using Green's Theorem for Vector Fields

1. Apr 11, 2015

Calpalned

1. The problem statement, all variables and given/known data

2. Relevant equations
n/a

3. The attempt at a solution
I don't understand how the book went from calculating Green's theorem on $\int _c Pdx + Qdy + \int _{-c'} Pdx + Qdy =$ (1 in the attached picture) to getting (labeled 2) $\int _c Pdx + Qdy = \int _{c'} Pdx + Qdy$

Thank you

2. Apr 11, 2015

fourier jr

just work out the derivatives $\frac{\partial Q}{\partial x}$ & $\frac{\partial P}{\partial y}$ & use the fact that for a path C, $\int_{-C} P\,dx + Q\,dy = -\int_{C} P\,dx + Q\,dy$