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Oblain Fourier series for the function f(x)=πx,0≤x≤1 =π(2−x),1≤x≤2.
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written 3.0 years ago by |
Solution:
Let, f(x)=a02+∑∞n=1ancosnπx+∑∞n=1bnsinuπx
Then, a0=∫20f(x)dx=∫10πxdx+∫21π(2−x)dx=π[x22]01+π[2x−x22]12
=π(12)+π[(4−2)−(2−12)]=π
$$ \begin{aligned} a_{n} &=\int_{0}^{2} f(x) \cos n \pi x d x=\int_{0}^{1} \pi x \cos …