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Let C denote the rectangle with vertices (0,-2), (0, 2), (2,-2), and (2, 2), oriented counterclockwise. Find So COS TTZ 2²-1 dz

Let C denote the rectangle with vertices (0,-2), (0, 2), (2,-2), and (2, 2), oriented counterclockwise. Find So COS TTZ 2²-1 dz

Advanced Engineering Mathematics
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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Let \( C \) denote the rectangle with vertices \( (0, -2) \), \( (0, 2) \), \( (2, -2) \), and \( (2, 2) \), oriented counterclockwise. Find \[ \int_C \frac{\cos \pi z}{z^2 - 1} \, dz \]
Transcribed Image Text:Let \( C \) denote the rectangle with vertices \( (0, -2) \), \( (0, 2) \), \( (2, -2) \), and \( (2, 2) \), oriented counterclockwise. Find \[ \int_C \frac{\cos \pi z}{z^2 - 1} \, dz \]
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Step 1: Draw the contour C and find the poles with in C.

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