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(a) Let f(x) = 2 (3x² + 10iz - 3)² (i) Show that f has a pole of order 2 at the point -i/3, and evaluate the residue of f at -i/3. (ii) Use the strategy for evaluating real trigonometric integrals and the result from part (a)(i) to deduce that r2π So 1 (3 sint + 5)2 dt = 5T 32

(a) Let f(x) = 2 (3x² + 10iz - 3)² (i) Show that f has a pole of order 2 at the point -i/3, and evaluate the residue of f at -i/3. (ii) Use the strategy for evaluating real trigonometric integrals and the result from part (a)(i) to deduce that r2π So 1 (3 sint + 5)2 dt = 5T 32

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 (a) Let f(2)= (3z²+ 10iz - 3)²* Show that f has a pole of order 2 at the point -i/3, and evaluate the residue of f at -i/3. (ii) Use the strategy for evaluating real trigonometric integrals and the result from part (a)(i) to deduce that •2πT 1.th 1 (3 sint + 5)² (b) Use a method for summing series of even functions to prove that V3-5. IM8 10 (4n²-1) (9n² - 1) dt = - 5π 32
Transcribed Image Text:Question 1 (a) Let f(2)= (3z²+ 10iz - 3)²* Show that f has a pole of order 2 at the point -i/3, and evaluate the residue of f at -i/3. (ii) Use the strategy for evaluating real trigonometric integrals and the result from part (a)(i) to deduce that •2πT 1.th 1 (3 sint + 5)² (b) Use a method for summing series of even functions to prove that V3-5. IM8 10 (4n²-1) (9n² - 1) dt = - 5π 32
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