Let f = u + iv be a contiunous function and o(t) = x(t) + iy(t) be a piecewise smooth curve...
Show that Re{ integral (f(z) dz } = integral (udx - vdy)
How do I show this?
What have you tried? Also, you need to be more describitive. Are we trying to prove that $\displaystyle \text{Re}\int_\Gamma f(z) dz=\int_{\Gamma}\left(u\text{ }dx-v\text{ }dy\right)$?