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Question 1 Evaluate the following integrals using residue theorem: (a) L (2² +9) (1 dz (x²+9)(x²+4)² 2r³ sin ur (1+²)2 dr (e) CoS z Loo (7² + 1) (2²+4)² -dr Question 2 (a) By making appropriate use of Jordan's lemma, find the Fourier transform of f(x) -1)² (b) Find the Fourier-sine transform (assume k ≥ 0) for (b)

Question 1 Evaluate the following integrals using residue theorem: (a) L (2² +9) (1 dz (x²+9)(x²+4)² 2r³ sin ur (1+²)2 dr (e) CoS z Loo (7² + 1) (2²+4)² -dr Question 2 (a) By making appropriate use of Jordan's lemma, find the Fourier transform of f(x) -1)² (b) Find the Fourier-sine transform (assume k ≥ 0) for (b)

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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Question 1 Evaluate the following integrals using residue theorem: 2² L (x² + 9) (x² + 4)2¹a (b) 2r³ sin wr Lo (1 +2²) ² (c) cos r dr Loo (7² + 1)(x² + 4) d Question 2 (a) By making appropriate use of Jordan's lemma, find the Fourier transform of f(x) (x² + 1)²¹ (b) Find the Fourier-sine transform (assume k ≥ 0) for ~0
Transcribed Image Text:Question 1 Evaluate the following integrals using residue theorem: 2² L (x² + 9) (x² + 4)2¹a (b) 2r³ sin wr Lo (1 +2²) ² (c) cos r dr Loo (7² + 1)(x² + 4) d Question 2 (a) By making appropriate use of Jordan's lemma, find the Fourier transform of f(x) (x² + 1)²¹ (b) Find the Fourier-sine transform (assume k ≥ 0) for ~0
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