(a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the line segment [—R, R] and the upper semicircle SÅ that connects R to −R via iR. i. Evaluate the integral Sen ii. Use part i. to evaluate the real integral 1 (z² - 6z+25)² (You may use the inequality Von SR without proof.) 1 10 (47² - 6x + 25)² -∞ 1 (2² − 6z+25)2 dz ≤ - dz. dx. TR (R² – 6R – 25)² for all R > 5
(a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the line segment [—R, R] and the upper semicircle SÅ that connects R to −R via iR. i. Evaluate the integral Sen ii. Use part i. to evaluate the real integral 1 (z² - 6z+25)² (You may use the inequality Von SR without proof.) 1 10 (47² - 6x + 25)² -∞ 1 (2² − 6z+25)2 dz ≤ - dz. dx. TR (R² – 6R – 25)² for all R > 5
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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![(a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the
line segment [-R, R] and the upper semicircle SÅ that connects R to −R via iR.
i. Evaluate the integral
Sca
CR
ii. Use part i. to evaluate the real integral
SR
without proof.)
(You may use the inequality
V₁
1
(z² - 6x +25)²
∞
1
Lulet - 6x + 2515 ²:
dx.
88
1
- 6z +25)²
dz.
dz/s
TR
(R² - 6R - 25)²
for all R 5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0d2dbea-0987-4c02-a00c-0b87f219c8f9%2F7f1f1437-462d-4a81-8e51-68461286f555%2Fo6f1uxc_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let R > 5 and let CR be the closed, anticlockwise contour obtained by joining the
line segment [-R, R] and the upper semicircle SÅ that connects R to −R via iR.
i. Evaluate the integral
Sca
CR
ii. Use part i. to evaluate the real integral
SR
without proof.)
(You may use the inequality
V₁
1
(z² - 6x +25)²
∞
1
Lulet - 6x + 2515 ²:
dx.
88
1
- 6z +25)²
dz.
dz/s
TR
(R² - 6R - 25)²
for all R 5
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