Question

8- Find the Fourier series of f(x)=x in (0,2π)​

Answer 1

I will briefly explain.

2.FOURIER COSINE SERIES:

A series said to be FOURIER COSINE SERIES which contain Fourier arbitrary constant ao, an and bn=0 if fx should be even function and interval lie between –pi to pi

2.1 EVEN FUNCTION:

A function y = f(x) is said to be even, if f(-x) = f(x). The graph of the even function is always symmetrical about the y-axis.

3.FOURIER SINE SERIES

A series is said to be FOURIER SINE SERIES which contain Fourier arbitrary constant bn and ao=an=0 if fx should be odd function and interval lie between –pi to pi.

ODD FUNCTION:

A function y=f(x) is said to be odd, if f(-x) = – f(x). The graph of the odd function is always symmetrical about the origin. For example, the function f(x) = in [-1,1] is even as f(-x) = = f(x) and the function f(x) = x in [-1,1] is odd as f(-x) = -x = -f(x).