Verify orthogonality integral by direct integration

[physcisgirl]

This is a heat equation related math problem.
1. Homework Statement
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.

Homework Equations

κ*λ_n*cos(λ_n*a) + h*sin(λ_n*a)=0.

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!

 

[BvU]

Hello PG,

Seems to me you think we know what the context of your partial problem statement is, but we're pretty lousy at telepathy. Please provide some more context -- where does this exercise appear, what do the variables stand for, etc.