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## Homework Statement

The question is here:

http://ocw.mit.edu/courses/mathemat...ions-fall-2006/assignments/probwave1solns.pdf

It's a long question and I figured attaching the link here would be better.

I need help with the question on page 4.

when

U

_{t}(x,0)=g(x)

and U(x,0)=0

## Homework Equations

The only relevant equation is the integral of Integral[ g(s)ds,s,x-t,x+t]

## The Attempt at a Solution

I tried to look at the solutions but I don't understand how to find the boundaries of the integral from the regions.

for example,

to be in region 2, the solution says that x+t>1 and -1<x+t<1

why is that ?

how was this derived ?

Thanks,

Roni.