Prove the following integrals. a) z l 0 sin nï l x sin mï l x dx = 0 if n 6= m l

Prove the following integrals. a) z l 0 sin nï l x sin mï l x dx = 0 if n 6= m l 2 if n = m
b) z l 0 cos mï l x dx = l if m = 0 0 if n ⥠1
c) z l 0 cos nï l x cos mï l x dx = 0 if n 6= m l 2 if n = m
d) z l âl cos nï l x cos mï l x dx = 0 if n 6= m l if n = m
e) z l âl sin nï l x sin mï l x dx = 0 if n 6= m l if n = m
f) z l âl sin nï l x cos mï l x dx = 0 for all n, m ⥠1