Solving the Fourier cosine series

[chwala]

Homework Statement

Kindly see attached (just need clarification on highlighted part).

Relevant Equations

Fourier cosine series

My question is; is showing the highlighted step necessary? given the fact that $\sin (nπ)=0$? My question is in general i.e when solving such questions do i have to bother with showing the highlighted part...

secondly,

Can i have $f(x)$ in place of $x^2$? Generally, on problems to do with Fourier series- what is usually indicated is $f(x)$... or it does not matter? yes, i know that $f(x)=x^2$. My question is in reference to the general widely used notation on such problems.

Cheers.

 

[Mark44]

My question is; is showing the highlighted step necessary? given the fact that sin⁡(nπ)=0? My question is in general i.e when solving such questions do i have to bother with showing the highlighted part...

Yes, it's necessary, IMO. Otherwise, the transition from the line above the highlighted line to the one below it would be harder to follow. Several people have made comments in some of your threads that it was difficult to follow your work because of omitted steps.

Can i have f(x) in place of $x^2$?

Why would you want to? Since you're finding the Fourier series of $x^2$, why hide this fact by calling it f(x)?