This is a heat equation related math problem. 1. The problem statement, all variables and given/known data The complete question is: Verify the orthogonality integral by direct integration. It will be necessary to use the equation that defines the λ_n: κ*λ_n*cos(λ_n*a) + h*sin(λ_n*a)=0. 2. Relevant equations κ*λ_n*cos(λ_n*a) + h*sin(λ_n*a)=0. 3. The attempt at a solution I tried to integrate the above given equation, but it doesn't really make sense to me to integrate it. I'm not sure what orthogonality integral it wants me to integrate. I think it's related to fourier series sine and cosine, I also googled orthogonality integral, but couldn't find what I'm looking for. Any help for clarifying and how I should tackle this question would be greatly appriciated!