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SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п

SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п

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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show that the fourier series of the function ?(?) = |?| ?? [−?, ?] is : 

(2((-1)" – 1) an? x – 6n si 6n<x< 7n ={ x si 7n < x < 8n cOs nx n=1
Transcribed Image Text:(2((-1)" – 1) an? x – 6n si 6n<x< 7n ={ x si 7n < x < 8n cOs nx n=1
Expert Solution
Step 1

The Fourier series of the function fx on -L,L is as follows.

fx=a0+∑n=1∞ancosnπxL+bnsinnπxL.

Use the following formulae to calculate the Fourier coefficients of the function fx on the interval -L,L.

a0=12L∫-LLfxdxan=1L∫-LLfxcosnπxLdxbn=1L∫-LLfxsinnπxLdx

 

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