Here I got a question of Fourier series attached with this. Also I atemped some part of the question (that is attached here with) but I need to know is this answer is correct.. or not
and how I prove the part b) from the above result.
Here I got a question of Fourier series attached with this. Also I atemped some part of the question (that is attached here with) but I need to know is this answer is correct.. or not
and how I prove the part b) from the above result.
When now i calcalate this again as considering even function
then $\displaystyle b_n=0$
$\displaystyle a_0=\frac{2}{\pi}\int\limits_{0}^{\pi} f(x) dx $
$\displaystyle =\frac{2}{\pi}\int\limits_{0}^{\pi/2}(1)dx+\frac{2}{\pi}\int\limits_{\pi/2}^{\pi/2}0dx+\frac{2}{\pi}\int\limits_{\pi/2}^{\pi}(-1)dx$
$\displaystyle =(1-\frac{\pi}{2})$
$\displaystyle a_n=\frac{2}{\pi}\int\limits_{0}^{\pi}f(x)Cos nx dx$
$\displaystyle =\frac{2}{\pi}\int\limits_{0}^{\pi/2}1.Cos.nx.dx+\frac{2}{\pi}\int\limits_{\pi/2}^{\pi/2}.0.Cos.nx.dx+\frac{2}{\pi}\int\limits_{\pi/2}^{\pi}(-1).Cos.nx.dx$
$\displaystyle =\frac{2}{\pi}(\frac{Sinn(\pi/2)}{n})+\frac{2}{\pi}(\frac{-Sinn\pi}{n}+\frac{Sinn\pi}{2n})$
=0
Is this calculation is true? otherwise plz show me the incorrect place..