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(Solved): 2. (10pts) Let (x)x2 for 0x1=l. (a) Calculate its Fourier sine series. (b) Calculate its ...

$2. \( (10 \mathrm{pts}) \) Let \( \phi(x) \equiv x^{2} \) for \( 0 \leq x \leq 1=l \). (a) Calculate its Fourier sine series.$

2.

(10 pts)

Let

ϕ (x) \equiv x^{2}

for

0 \leq x \leq 1 = l

. (a) Calculate its Fourier sine series. (b) Calculate its Fourier cosine series.

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Solution :

(a) The Fourier sine series of is given by :

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