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b) Using the Residue Theorem (or otherwise) compute the follo- wing integrals (all the curves are positively oriented; state all the theorems/propositions that are used in the solution) A ez dz 2²++ dz i) S ½-½ e² dz iii) ) (2-1)² (2+1) 2 Z2+1 121=12²-22 i) S 121=1 iv) S sinz 121=2 (2+1) 3 dz S dz 12-1-11=2 v) 12-11=5 (2-5) (2+1) 9

b) Using the Residue Theorem (or otherwise) compute the follo- wing integrals (all the curves are positively oriented; state all the theorems/propositions that are used in the solution) A ez dz 2²++ dz i) S ½-½ e² dz iii) ) (2-1)² (2+1) 2 Z2+1 121=12²-22 i) S 121=1 iv) S sinz 121=2 (2+1) 3 dz S dz 12-1-11=2 v) 12-11=5 (2-5) (2+1) 9

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) Using the Residue Theorem (or otherwise) compute the follo- wing integrals (all the curves are positively oriented; state all the theorems/propositions that are used in the solution) A ez dz 2²++ dz i) S ½-½ e² dz iii) ) (2-1)² (2+1) 2 Z2+1 121=12²-22 i) S 121=1 iv) S sinz 121=2 (2+1) 3 dz S dz 12-1-11=2 v) 12-11=5 (2-5) (2+1) 9
Transcribed Image Text:b) Using the Residue Theorem (or otherwise) compute the follo- wing integrals (all the curves are positively oriented; state all the theorems/propositions that are used in the solution) A ez dz 2²++ dz i) S ½-½ e² dz iii) ) (2-1)² (2+1) 2 Z2+1 121=12²-22 i) S 121=1 iv) S sinz 121=2 (2+1) 3 dz S dz 12-1-11=2 v) 12-11=5 (2-5) (2+1) 9
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