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4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

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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I want a detailed solution for integration Example Expand f(x) = x, 0<x < 2 in a half range a (b) cosine series (0) To get a cosine series the function must be an even function. So, we extend the given function to have an even function. This is called the even extension of J(x). T = 4 27 O, = %3D Since now the function is even then b, = 0 2. d, = T. 1 x %3D xdx = = 1 2 2 4 T12 Ss(x) cos(no,r kdx= rcos dx 2 an %3D nt.x sin (1) 11 t cos 0. п even 4 (cos(n7)-1)= - 8 11 odd Then f(x)= d, + 4 (cos(n7)-1)cos
Transcribed Image Text:I want a detailed solution for integration Example Expand f(x) = x, 0<x < 2 in a half range a (b) cosine series (0) To get a cosine series the function must be an even function. So, we extend the given function to have an even function. This is called the even extension of J(x). T = 4 27 O, = %3D Since now the function is even then b, = 0 2. d, = T. 1 x %3D xdx = = 1 2 2 4 T12 Ss(x) cos(no,r kdx= rcos dx 2 an %3D nt.x sin (1) 11 t cos 0. п even 4 (cos(n7)-1)= - 8 11 odd Then f(x)= d, + 4 (cos(n7)-1)cos
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