2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countours. C2 C3 120° |= x=0 1 dx x3+1 а- R C1 Figure of section a C2 C3 b-l= J-0 x=0 x4+1 Figure of section b

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel
integrals for a given countours.
C2
C3
a-l=o dx
1
120°
x=0
x3+1
R
Figure of section a
C2
C3
b-l=Jx=0
x4+1
R
C1
Figure of section b
(Hint: Firstl consider complex form of integral
For example : In section a, Se dz , show that S. (..) = I and SoC.) = 0 . For
Sa(...), find the relationship between S.(...) and I by using z=R eio transform .Finally
z3+1
find the I thanks to 2ni E Residue =
Transcribed Image Text:2- Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel integrals for a given countours. C2 C3 a-l=o dx 1 120° x=0 x3+1 R Figure of section a C2 C3 b-l=Jx=0 x4+1 R C1 Figure of section b (Hint: Firstl consider complex form of integral For example : In section a, Se dz , show that S. (..) = I and SoC.) = 0 . For Sa(...), find the relationship between S.(...) and I by using z=R eio transform .Finally z3+1 find the I thanks to 2ni E Residue =
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