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## Homework Statement

Use d'Alembert's formula to solve the boundary value problem for a string of unit length, subject to the given conditions.

I can't get this to work with LaTeX so I hope this makes sense.

f(x) = 2x if 0 ≤ x ≤ 1/2

f(x) = 2(1-x) if 1/2 < x ≤ 1

g(x) = x

c=1

## Homework Equations

[tex]u(x,t)=\frac{1}{2}[f^{*}(x-ct)+f^{*}(x+ct)]+\frac{1}{2c}\int^{x+ct}_{x-ct}g^{*}(s)ds[/tex]

## The Attempt at a Solution

I've been able to do previous problems up until this one. Previous problems were all a single function that was 2 periodic. This one I am not sure where to start. I at least thought the g

^{*}wouldn't be too hard since it's only x, but there is an example that shows the same thing and they have completely different integration limits.

I think my whole problem is even/odd extensions. I am not the best at them and plan to go back and study them again since they are a couple sections back.

Any tips to get this one even started?