Question

Evaluate the following complex integral.

∫γ f(z) dz
Given:
f(z) = 1; γ(t) = t^2−it for 1 ≤ t ≤ 3.

Answer 1

* 5. Use Cauchy's Integral formula and 1. to calculate:

z7+1 a) Sdz where y(t) = 2 + et, 0 ≤t ≤ 2π.

b) Sdz where y(t) = −i + e², 0 ≤ t ≤ 2π.

c) Jdz where y(t) = 3eit, 0 ≤t ≤ 2π.