Cn coefficient for a Fourier series

[sekowe]

Homework Statement

I have an example were they determine the Cn coefficient for a Fourier series:

My problem is i don't follow what happens in the following moment:

neither am i sure how the two e^-inwt comes to be cos(nwt) in the last part.

Homework Equations

The Attempt at a Solution

The only solution I can come up with is to reverse the limits what is obvious and then say: t=-a --> -1*t=-1*-a and then change a for -a in the limit and t for -t. However this doesn't work in other similar problems so I don't think think this is right.

 

[tiny-tim]

welcome to pf!

hi sekowe! welcome to pf!

there's a misprint

the first exponent in the third line should be positive

between the second and third lines, they've substituted u = -t, du = -dt, and then renamed u as t again!

and of course the corrected third line let's you use e^ix + e^-ix = (cosx)/2

 

[sekowe]

A misprint... Yeah that clears up a lot :D

Thank you very much!