Use the theory of residues to evaluate the following real, definite integrals: 210 do Hint: integrate...
Exercise 12: Residues and real integrals (a) [6+4 points) Compute the residues for all isolated singularities of the following functions (i) f(2)== (2-) tan(2), (i) 9(2):= z2 sin () (b) (4+6+5 points) Compute (using the Residue theorem) (1) cos(72) ( d, A3 := {z € C:<3), 243 := {Z EC: | = 3}, 34, (2-1)(2 + 2)2(2-4) : 43 € C:21 <3}, po 12 To (x2 + 4)2 da, 24 2 + 4 cosat. J 5 + 4 sin(t)
use residue theorem to evaluate the following integrals 16) cosa 30 de 5- 4 cos 20 17) COSI det (x + 1)? sin 3x dx 18) sin x dx (x² + 4x+5 19)
the previous hw question and answer 1. Consider the integral from question 2 of the previous homework assignment: too sin ma dx, and assume that both m and a are positive real numbers. By using an indented contour, evaluate this integral fully. You are allowed to resubmit material submitted as part of the previous assignment if you wish.] 2. (30 marks] Evaluate the following integrals: too sin ma x(x2 + a2) dar, m, a real, a +0. rt eike dx,...
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...