2- Assume that x, y ER and z = x+ iye C and answer the followings. Calculate the reel integrals for a given countours. (Hint: Firstl consider complex form of integral For example : In section a, S. dz, show that f (...) = 1 and So...) = 0. For Sa(.…..), ind the relationship between fe (...) and I by using z=R et transform .Finally find the I thanks to 2ni E Residue = Se.c..(...) ) C2 1 dx x3+1 00 120° a- l= R Figure of section a b-l= Jx=0 x*+1 Figure of section h

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Calculate the reel integrals for a given countour in figure 1 .

2- Assume that x, y ER and z = x + iy e C and answer the followings. Calculate the reel
integrals for a given countours.
(Hint: Firstl consider complex form of integral
For example : In section a, S dz, show that f. ...) = I and S(..) = 0 . For
Sa .), ind the relationship between f....) and I by using z=R ete transform .Finally
find the I thanks to 2ni E Residue = Sero.+c,(.) )
C2
C3
a- l=o dx
00
1
a- I=
120
Jx30 x3+1
R
Figure of section a
C2
b-l=o dx
00
-dp-
x=0 x4+1
Figure of section b
Transcribed Image Text:2- Assume that x, y ER and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countours. (Hint: Firstl consider complex form of integral For example : In section a, S dz, show that f. ...) = I and S(..) = 0 . For Sa .), ind the relationship between f....) and I by using z=R ete transform .Finally find the I thanks to 2ni E Residue = Sero.+c,(.) ) C2 C3 a- l=o dx 00 1 a- I= 120 Jx30 x3+1 R Figure of section a C2 b-l=o dx 00 -dp- x=0 x4+1 Figure of section b
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