# Peicewise Smooth curve

• Mar 15th 2010, 01:10 PM
jzellt
Peicewise Smooth curve
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?
• Mar 15th 2010, 01:17 PM
Drexel28
Quote:

Originally Posted by jzellt
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 $\text{Re}\int_\Gamma f(z) dz=\int_{\Gamma}\left(u\text{ }dx-v\text{ }dy\right)$?
• Mar 15th 2010, 01:30 PM
jzellt
Yes, that I want Im trying to show.

I really don't know how to approach this problem, so I havn't done anything.

I was hoping to see how this one is done so I can do a similiar proof (the imaginary part) by myself...