Page 31 - E-Modul Fisika Matematika Materi Deret Fourier

x
1 L n
a   f ( x cos dx
)
n
L L
L
1  0 n L n x 
x

a n    f (x ) cos dx  f (x ) cos dx 
L L L 
L 0
1  0 n (x ) L n 
x

a    f (x ) cos d (x )  f (x ) cos dx

n
L L L 
L 0
1  L n x L n 
x

 f
a    (x ) cos dx  f (x ) cos dx   0
n
L  0 L 0 L 
x
1 L n
b n   f ( x sin dx
)
L L L
x
x
1  0 n L n 

b n    f ( x sin dx  f ( x sin dx 
)
)
L L L 0 L 

1  0 n ( x) L n x 

)
)
b n    f ( x sin d( x)  f ( x sin dx 
L L L 
L 0
1  L n x L n x 

b    f ( x sin dx  f ( x sin dx 
)
)
n
L L L 
 0 0
2 L n x
)
b   f ( x sin dx
n
L L
0
Namun, jika (xf ) adalah fungsi genap maka berlaku:

maka f(x) “dikatakan” diperluas dalam deret cosinus fourier.

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