If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the Residue theorem
If I = may be Evaluate I 20 do 1-2p000 + p² written using show that it 3=eja dz (1-P3)(3-P) of the Residue theorem
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
![If
\[ I = \int_0^{2\pi} \frac{d\theta}{1 - 2p \cos \theta + p^2} \]
show that if \( z = e^{i\theta} \)
\[ I \] may be written as
\[ \oint \frac{dz}{(1 - pz)(z - p)} \]
Evaluate \( I \) using the Residue Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71f6a4b8-527f-4030-b85a-828002701c6f%2F933d15f9-5bff-42fe-a732-d86c694ebbf9%2Funmpp5h_processed.png&w=3840&q=75)
Transcribed Image Text:If
\[ I = \int_0^{2\pi} \frac{d\theta}{1 - 2p \cos \theta + p^2} \]
show that if \( z = e^{i\theta} \)
\[ I \] may be written as
\[ \oint \frac{dz}{(1 - pz)(z - p)} \]
Evaluate \( I \) using the Residue Theorem.
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