8. Evaluate the following integrals using the residue theorem: r sin r dr. x² +1 x² +1 2+1 -8 dr. x (x²+2x+2)(x²+4) -dz
8. Evaluate the following integrals using the residue theorem: r sin r dr. x² +1 x² +1 2+1 -8 dr. x (x²+2x+2)(x²+4) -dz
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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Question
Transcribed Image Text:8. Evaluate the following integrals using the residue theorem:
x sin x
L
T
2π
x² +1
x² +1
2+1
dr.
dr.
(x²+2x+2)(x² + 4)
cos
2 + cos 0
-dx
de
Use Rouché's theorem to determine the number of zeros (counting multiplicities) in the unit
disk, of the equation:
z" +82² +1 = 0, n E, n ≥ 3.
24 +2³-4z + 1 = 0 in the annulus 1 < |2|< 3.
Expert Solution
Step 1: Q-8 Part-1
Since there are many questions, find the solutions to the first three parts of the first question.
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