00:01
So, first of all we need to find out the fourier coefficient of the function f of x is equals to 8x plus 8, numbers a naught, bk, ck we know they are the coefficients and f of x is given to be equals to a naught times 1 over root 2 plus b1 times of sine x plus c1 times cosine of x plus b2 times sine 2x and so on.
00:30
So, let us try to find out what is the value here.
00:36
So, for this we know the formula for a naught over root 2 it is given by 1 over 2 pi integral from minus pi to pi integrate the function which is 8x plus 8 times of bx.
00:51
So, 1 over 2 pi here we are going to have 8x square over 2 plus 8 times of x limit from minus pi to pi.
01:01
So, solving this we are getting 1 over 2 pi times 16 pi.
01:07
So, which is nothing but equals to 8.
01:10
So, from this i get a naught over root 2 is equals to 8 which implies a naught value is 8 times of root 2.
01:20
Now, we have to find what is the value of bk and we know that bk value is given by 1 over pi integral from minus pi to pi 8x plus 8 times sine kx dx.
01:38
Now, what we are going to do we can apply integration by parts here...