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Given the Fourier sine series of $(x) = x as show that the series can be integrated b) Find The Fourier cigine Series for 27²/2. Find the constant of integration. c) By setting e (1) he n=1 n² n2 on (0₁1) term by term. x=0, find the sum

Given the Fourier sine series of $(x) = x as show that the series can be integrated b) Find The Fourier cigine Series for 27²/2. Find the constant of integration. c) By setting e (1) he n=1 n² n2 on (0₁1) term by term. x=0, find the sum

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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Given the Fourier sine series of $(x) = x on (0₁1), a) & I show that the series can be integrated term by term. b) Find The Fourier cigine Series for 27/2. Find the constant of integration. c) By setting e Edhel n=1 n² solution. x = 2 (-1)" 00 mal C = 40 = 2 Integration of both sides gives Stdt = 22²/2 x=0, find the sum or mtl 77² ze sin (mix/l) mti Constant of integration is the missing coefficient = √₁² =²dx = £² é o 6 T2 We X=0 ( kowe 4 by selling 0=l¾ 2= 1² + 2 (-j² 21² m m=1 m²T1² 00 = C + Σ (-1) mal ze² cos (mitx/e) M²T72 = 2 (-15mel 1 mal m²
Transcribed Image Text:Given the Fourier sine series of $(x) = x on (0₁1), a) & I show that the series can be integrated term by term. b) Find The Fourier cigine Series for 27/2. Find the constant of integration. c) By setting e Edhel n=1 n² solution. x = 2 (-1)" 00 mal C = 40 = 2 Integration of both sides gives Stdt = 22²/2 x=0, find the sum or mtl 77² ze sin (mix/l) mti Constant of integration is the missing coefficient = √₁² =²dx = £² é o 6 T2 We X=0 ( kowe 4 by selling 0=l¾ 2= 1² + 2 (-j² 21² m m=1 m²T1² 00 = C + Σ (-1) mal ze² cos (mitx/e) M²T72 = 2 (-15mel 1 mal m²
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