622 Higher Engineering Mathematics
in the range 0 to 2π.y0211 2 Figure 67.5- Sketch the waveform defined by:
f(x)=⎧
⎪⎪
⎨
⎪⎪
⎩1 +2 x
π, when−π<x< 01 −
2 x
π, when 0<x<πDetermine the Fourier series in this range.⎡⎢
⎢
⎣f(x)=8
π^2(
cosx+1
32cos3x+1
52cos5x+1
72cos7x+···)⎤
⎥
⎥
⎦- For the Fourier series of Problem 8, deduce a
series for
π^2[^8
π^2
8= 1 +
1
32+
1
52+
1
72+
1
92+···]