1. Compute the following integrals where m and n are non-negative integers. Look out for special cases.
(a) ∫ 0 --> L cos(n pi x/L)cos(m pi x/L) dx
(b) ∫ 0 --> L cos(n pi x/L)sin(m pi x/L) dx
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Integrals are computed and special cases are considered. The solution is detailed and well presented.