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Complex integration based on residual theorem , Exercises of Mathematics

Al-Aqsa UniversityMathematics

Complex integration based on residual theorem

Typology: Exercises

2017/2018

Uploaded on 01/06/2018

OSAMA-ALSATTARI
OSAMA-ALSATTARI 🇵🇸

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[ea] ax Exercise: Use the residual theory to evaluate | G+ NGA) Solution: Letx* +9 =0,774+4=0> 4% = +2i,43i Since x = 21, 3iare inthe upper half of the circle we use it. 1 (z—20)(2+ 202249) 20i 1 1 @—3)@+3p@+4) 305 First, Res(f,2i) = lim (z — 2i) iat Second, Res(f,3i) = lim (z — 3i) fal ( ax mf 1 1 As & consequence, 4G? 4) = 2ni (sei ) mci 20i 30i/ 30 + 9)(x? + 4) =o