Question

Choose three questions to do

The first method:

the second method

thank you

19-29 INTEGRATION Integrate by the first method or state why it does not apply and then use the second method. (Show the details of your work.) 19. | Re z dz, C the shortest path from 0 to 1 + i 20. J Re z dz, C the parabola y from 0 to 1 + i 21. | e2z dz, C the shortest path from Ti to 2πί 22. sin z dz, C any path from 0 to 2i 23. I cos2 z dz from _πί along Iz|-π to πί in the right "С half-plane 24. ( z1) dz, C the unit circle (counterclockwise) 25. | cosh 4zdz, Cany path from-m/8 to π1/8 . First Eaution methool sinaple c losaol curve in hnp Points t impla closed Curve impw con (cortus on C 424 d2 t).dt dt Cr

Answer 1

La path frcom o to . (ti) On C 2- = (Iti ) uina methv

Rende, cis tne parcasole 0

path from Ti to 270 , 271 2兀 冗 兀 2- 당〈

(22 From o to 21 , put 2= χ-tur 2u 0 42 2. ( Sin2d): F Siol.nrtiy)(t(X-t id y丿 0 0 2. 2.