00:01
Hello students, the fourier series for a given function fx, the fourier series for a given function fx, for a given function f of x with period 2l is given by fx equal to a0 by 2 n plus summation n equal to 1 to infinity a n cos 2 n pi x by l 2l plus b n sin 2 n pi x by 2l where a0 equal to 1 by l integration minus l 2 l fx dx, a n equal to 1 by l integration minus l 2 l fx cos square n pi x by 2l dx and b n equal to 1 by l integration minus l 2 l fx sin 2 n pi x by 2 l dx, this is cos 2 n pi x by 2 l.
01:37
So, now we evaluate the values.
01:40
So, first we evaluate a0.
01:42
So, a0 equal to 1 by 4 into since the period is 4 minus 2 to 0, 0 dx plus integration 0 to 1 x dx plus integration 1 to 2, 1 dx.
02:05
So, if we calculate this we have this is equal to 3 by 4.
02:11
Now, here since x belongs to minus 2 to 2.
02:20
So, the period is l equal to 2l equal to 4.
02:29
So, for the next we calculate a n...