1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R → 00, C e (-R,+R) ) Im{2} x2 a- S x=-∞ x4+1 ax Re(z} R b- Sr-o (x2+1)? x2 Figure 1 x=-∞ (x²+1)² cos(2x) dx x=-∞ (x²+1)² C- sin(2x) d- x=-∞ (x2+1)² x xsin(x) e- е- x=-∞ (x²+1)(x²+4)
1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals for a given countour in figure 1 .(Consider R → 00, C e (-R,+R) ) Im{2} x2 a- S x=-∞ x4+1 ax Re(z} R b- Sr-o (x2+1)? x2 Figure 1 x=-∞ (x²+1)² cos(2x) dx x=-∞ (x²+1)² C- sin(2x) d- x=-∞ (x2+1)² x xsin(x) e- е- x=-∞ (x²+1)(x²+4)
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 31E
Related questions
Question
please only calculate a) and b). ignore the hint
![1-) Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel
integrals for a given countour in figure 1.(Consider R → 0, C € (-R,+R) )
Imfz}
x2
a- S-o dx
∞ x4+1
Re(z}
-R
R
b- Se-o (x²+1)?
Figure 1
X=-∞
cos(2x)
dx
C-
:- 00
sin(2x)
x=-∞ (x²+1)²
xsin(x)
dx
-Sr=- x²+1)(x²+4)
(Hint: In section c , firstly calculate Jcz2+4
eiz
dz for a given
countour.Then take the real part of result by using euler's
formula.You can use same strategy for section d and e by
considering imaginary part of result.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9811b3a5-0124-40a6-a8f0-2d01405602f2%2F98bb440f-80a0-417e-9245-951fbc983684%2Fvb5uk82m_processed.png&w=3840&q=75)
Transcribed Image Text:1-) Assume that x, y E R and z = x + iy E C and answer the followings. Calculate the reel
integrals for a given countour in figure 1.(Consider R → 0, C € (-R,+R) )
Imfz}
x2
a- S-o dx
∞ x4+1
Re(z}
-R
R
b- Se-o (x²+1)?
Figure 1
X=-∞
cos(2x)
dx
C-
:- 00
sin(2x)
x=-∞ (x²+1)²
xsin(x)
dx
-Sr=- x²+1)(x²+4)
(Hint: In section c , firstly calculate Jcz2+4
eiz
dz for a given
countour.Then take the real part of result by using euler's
formula.You can use same strategy for section d and e by
considering imaginary part of result.)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Elementary Linear Algebra (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781305658004/9781305658004_smallCoverImage.gif)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning