Solving D'Alambert Problem - Integrating g(x)

[Carolyn]

Homework Statement

please see the attachement

Homework Equations

Could somebody explain how to get the the system of equations at the bottom of the page from integrating g(x)?

The Attempt at a Solution

I attempted to integrate, but couldn't get the right answer, do I need to subtract the previous integration from the current one?

 

[quasar987]

Just so you know, we can't download your attachment until a mentor approves it.

 

[Carolyn]

g(x) = 1 when -1 < x < 1, and g(x) = 0 otherwise

how do I get

u(x,t) = (x+at+1)/2a for -1-at < x < -1+at
= t for -1+at < x < 1-at
= (1-x+at)/2a for 1-at< x<1+at

Thanks