1. The problem statement, all variables and given/known data Calculate the following integrals on the given paths. Why does the choice of path change/not change each of the results? (a) f(z) = exp(z) on i. the upper half of the unit circle. ii. the line segment from − 1 to 1. 2. Relevant equations ∫γf(z) = ∫f(γ(t))γ'(t)dt, with the limits being the limits of the parametrization. 3. The attempt at a solution i) γ(t) = eit, t ∈ [0, π] Integral = ∫ez dz = ∫eeitieitdt u substitution: u = eit, du = ieit => Integral =∫eudu, I leave the lower bound at 0 and upper bound at π because I'm going to substitute for u at the end. Integral = eu]0π = eeit]0π = eeiπ - ee0 = eeiπ - e1 = eeiπ - e ii) γ(t) = t, t ∈ [-1, 1] Integral = ∫e2 (1) dt, with lower bound = -1, upper bound = 1. = et ]-11 = e1 - e-1 = e - 1/e So the path does matter because two different paths gave two different answers. Whats wrong with my answer?