just answer Question 5 Show that Igamma f agrees with the us

just answer Question 5

Show that I_gamma, f agrees with the usual definition of integral_gamma f if gamma is piewise smooth. Let f be holomorphic on an open set u and p, q elementof u. If gamma, Psi: [a, b] rightarrow u are continuous curves from p to q that are close together, show that integral_gamma f = integral_Psi f.

Solution

Use cauchy integral formula to show that integral of a holomorphic function over a closed path is 0. Then it is obvious.