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Expand the function f(x) in Fourier series 4x(x - 1), = -{ 4x(1+x), 0≤x≤1 1 ≤ x ≤ 0,

Expand the function f(x) in Fourier series 4x(x - 1), = -{ 4x(1+x), 0≤x≤1 1 ≤ x ≤ 0,

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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Expand the function f(x) in Fourier series = 4x(x - 1), 4x(1+x), 0≤x≤1 −1≤ x ≤0,
Transcribed Image Text:Expand the function f(x) in Fourier series = 4x(x - 1), 4x(1+x), 0≤x≤1 −1≤ x ≤0,
Expert Solution
Step 1

Let us consider the function f(x) in the interval [-L,L]

The Fourier series of the function is 

f(x)=a0+∑n=1∞ancosnπxL+bnsinnπxL

Where,

a0=12L∫-LLf(x)dxan=1L∫-LLf(x)cosnπxLdxbn=1L∫-LLf(x)sinnπxLdx

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