I need to find the total number of states in a 1D monatomic lattice using the density of state equation g(ω), and I am having a hard time doing so. I'm fairly certain all I need to do ins integrate it, but this is proving to be a greater challenge than I thought it would. g(ω)=2L/(πaωm)*sec(qa/2). I'm almost positive if I integrate from 0 to ωm in terms of q, I will find the solution. However, every time I try, I get some crazy answer. what am I doing wrong?