1 2 3 P LK 111 LLL KKK K 246 Evaluate the following integrals, for a path y that travels from -Ti to Ti in the right half-plane, and also for a path y from -i to i in the left half-plane. (a) zdz (b) Syezdz (c) co cos z dz (d) J, sinh zdz Solution The integrals are all independent of path and can be evaluated by finding a primitive. (a) (b) z dz 2 (i) 5 (-2)5 25i == = = 5 5 5 5 edz = [e]i = ei ei = 1 (1) = 0. Ledz = (c) Loo cos z dz = [sin z]ki = ei(ni) - e-i(ni) - sin (Ti) sin (-i): == ei(-i)-e-i(-i) = 22 22 2 (e - e") = = i (e" e). 22 - (d) Lsin = sinh z dz = [cosh z] = cosh (Ti) cosh(z) = e-i +-(-i) 2 = 0.