Question

If f(x) is a periodie function with period 2L defined in the interval
C to C + 2L then Fourier coefficient ai is​

Answer 1

Answer:

ANSWER IS

0000

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Answer 2

Answer:

Fourier series of the function f(x) of period 2L can be written as

        $f(x) = a_{0} + \sum_{n=1} ^{\infty} (a_{n} cos\frac{n\pi x}{L} + b_{n} sin\frac{n\pi x}{L} )$  .......................(i)

Fourier coefficient in the interval c to c+2L is given by,

$a_{0} = \frac{1}{2L} \int\limits^{c+2L}_c {f(x)} \, dx$

$a_{n} = \frac{1}{L} \int\limits^{c+2L}_c {f(x) cos \frac{n \pi x}{L} } \, dx$         n = 1,2,3............

$b_{n} = \frac{1}{L} \int\limits^{c+2L}_c {f(x) sin \frac{n \pi x}{L} } \, dx$         n= 1,2,3,.............