# Homework Help: Showing the temperature distribution in an infinitely long cylinder

1. Oct 10, 2011

### Rubik

1. The problem statement, all variables and given/known data
Show that the temperature distribution in an infinitely long cylinder of metal with insulated sides and initial distribution

u(x, 0) = 0, the absolute value of x < L
u0, the absolute value of x > L

where u0 is a constant, is given for t >0, by

u(x, t) = (1/2)u0[2 - erf((x +L)/(√4c2t)) + erf((x - L)/(√4c2t))

2. Relevant equations

u(x, t) = 1/√4∏c2t∫e-(x - y)2/4c2t f(y) dy bounds = -∞<x<∞
3. The attempt at a solution

= (u0/√4∏c2t)∫e-(x - y)24c2tdy

Then I know you make a change of variables but I am having trouble with finding my new bounds of integration after I make the change of variables?

2. Oct 10, 2011

### Rubik

Relevent equation*

u(x, t) = (1/√4c2t)∫e-(x - y)2/4c2tf(y) dy

Attempt at a solution*

= u0/√4∏c2t)∫e-(x - y)2/4c2tdy

Then I know I need to make a change of variables but after I do that I am not sure how to determine the new bounds of integration?