00:01
We have to find the fourier series of the function fx is equals to x square in the interval minus pi to pi.
00:17
So, from here 2l is equals to the length of interval.
00:21
Length of interval is 2 pi.
00:24
So, l will be pi.
00:26
Assume that it's a fourier series is, fourier series is a0 by 2 plus summation of an cos n pi x by l plus summation bn sin n pi x by l.
00:59
Summation is moving from 1 to infinity in both.
01:06
Put l equals to pi here, we get a0 by 2 plus summation n equals to 1 to infinity of an cos nx plus summation n equals to 1 to infinity bn sin nx.
01:33
We will find out the values of a0, an and bn.
01:39
A0 is equals to 1 over pi integration from minus pi to pi of fx.
01:49
Fx is x square here.
01:51
So, x square ds.
01:54
After solving it, we will get 2 pi cube 2 pi square by 3.
02:03
Now, an.
02:04
An is equals to 1 by pi integration from minus pi to pi x square cos nx dx...