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Question Number 100899 by mhmd last updated on 29/Jun/20

f i n d t h e f o u r i e r s e r i e s o f t h e f u n c t i o n f (x) = {\begin{cases} x - 2 ⩽ x ⩽ 0 \\ 4 0 ⩽ x ⩽ 2 \end{cases} ?

h e l p m e s i r ?

Answered by bramlex last updated on 29/Jun/20

f (x) : o d d f u n c t i o n . L = 4

a_{n} = 0

b_{n} = \frac{2}{L} \underset{0}{\int^{L}} f (x) \sin (\frac{n π x}{L}) d x

b_{n} = \frac{2}{4} [\underset{- 2}{\int^{0}} x \sin (\frac{n π x}{4}) d x + \underset{0}{\int^{2}} 4 \sin (\frac{n π x}{4}) d x]

b_{n} = \frac{1}{2} [\frac{16}{n^{2} π^{2}} \sin (\frac{n π}{2}) + \frac{4}{n π}]

b_{n} = \frac{8}{{(n π)}^{2}} \sin (\frac{n π}{2}) + \frac{2}{n π}

f (x) = \frac{a_{0}}{2} + \underset{n = 1}{\sum^{\infty}} [\frac{8}{{(n π)}^{2}} \sin (\frac{n π}{2}) + \frac{2}{n π}] . \cos (\frac{n π x}{4})

Commented by mhmd last updated on 29/Jun/20

s i r c a n y o u s e n d t h e a l l s o l u t i o n ?

Commented by mhmd last updated on 29/Jun/20

t h a n k y o u s i r

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