I'm sorry if I came off as offended and defensive. I wasn't trying to.
I did notice after that you had the same identity written down as tiny tim, but I had already posted twice and didn't want to go back and post again.
I'll respond more carefully in the future so this doesn't happen again.
I am aware of the orthogonality relations, however I am not familiar with how they are derived, that is not covered in my textbook unfortunately. I do know that sin and cos are orthogonal on the interval -L to L, but they are not orthogonal on the interval 0 to L (according to my text), so this...
all i really need to do is solve the integral:
from x=0 to x=L
The Attempt at a Solution
I'm not very sure where to start with this. Any help would be appreciated.